However, the implicit shape method suffers from a low convergence speed and performs unstably due to the utilization of gradient-based optimization methods. Moreover, the implicit shape method requires priori information about the number of targets is not required anymore and the choice of step length is avoided.A shape-based reconstruction scheme of FMT with a cosinoidal level set method is proposed in this paper. The Heaviside function in the classical implicit shape method is replaced with a cosine function, and then the reconstruction can be accomplished with the Levenberg–Marquardt method rather than gradient-based methods. As a result, the Numerical simulations and phantom experiments were carried out to validate the proposed method. Results of the proposed method show higher contrast to noise ratios and Pearson correlations than the implicit shape method and image-based reconstruction method. Moreover, the number of iterations required in the proposed method is much less than the implicit shape method.The proposed method performs more stably, provides a faster convergence speed than the implicit shape method, and achieves higher image clarity than the image-based reconstruction method. Thanks to the ever-increasing fluorescent probes, proteins, and dyes, quantities of in vivo biomedical researches at cellular and subcellular levels are achieved noninvasively such as protein–protein interactions, protein function and gene expression –3. With The concept of FMT can be summarized as: the excitation and fluorescent light propagations in tissues are described with a certain mathematical model firstly, and then, a reconstruction scheme is conceived based on the minimization of the differences between fluorescent measurements and the corresponding predicted ones through the model. The two processes are generalized as two problems: forward and inverse problems . CommonlThe blurry images inhibit the applications of FMT in some occasions that need explicit boundaries . To dealpriori information about the number of reconstructed objects is essential for both of the two types of shape-based reconstruction methods. For the spherical harmonics expansion, a set of expansion coefficients can only describe a single object. Thus, multi-object reconstruction needs more than one set of expansion coefficients and each one needs to be initialized at the beginning of reconstruction , the value of fluorescent yield x(ψ) varies between xb and xf. Compared to Eq.  [b represents the matrix consisting of residual vectors on the right side of Eq. 17) are seration)  to obtaixb and xf can be acquired through the derivative of object function with respect to xb and xf:In parallel, the iteration equation for the fluorescent yields Ψ is updated through Eq. (xb and xf are updated through Eq. (ψ < 0 the level set function is set as 0. When ψ > 1 the level set function is set as 1.Equations  and 21)21) are uough Eq.  firstly,−1 and an absorption coefficient of 0.02 cm−1 was used to fill the cylindrical object to simulate the tissues. Accordingly, the fluorescent yields of the two targets used in the simulations were set to 1 and 0.6, respectively, and the optical coefficients were set as the same with the phantom experiments. For each group of the measurements, a line source was utilized to illuminate the cylinder along z-axis and 36 fluorescent images of different projection angles were acquired.In order to validate the performance of the proposed method, numerical simulations and phantom experiments were carried out. The geometry of the imaged object used in the simulations and phantom experiments was a cylinder with a diameter of 3 cm and a height of 5 cm as shown in Fig. priori information about the number of targets, i.e. only a single level set function was used and the fluorescent yield was initialized with a background coefficient xb and a single target coefficient xf.In reconstruction, the distributions of fluorescent yield at the central slice z = 2.5 cm were recovered through the proposed method, the classical image-based reconstruction method as well as the implicit shape method. The LM method was implemented to accomplish the iteration in the proposed and image-based reconstruction method, while the gradient descent method based on the artificial time evolution approach  was usedxi and xback denote the mean value of fluorescent yield within the true region of the ith target and the background, respectively. σi and σback are the corresponding variances. atar and aback represent the ratios of the areas, which are given as atar = Atar/A and aback = Aback/A, where Atar, Aback, and A denote the area of targets, the area of background, and the total area, respectively. T is the number of targets. Xtrue and Xrec are the vectors of fluorescent yield for the true and reconstructed distribution, respectively. The COV denotes the covariance and σ is the standard deviation. Higher CNR indicates better differentiability between the targets and the background, i.e. better image quality. The metric PC is used to describe the similarity between the true distribution and the reconstructed one. The CNRs and PCs of the reconstruction results of the simulation and phantom studies are listed in Tables The reconstruction results of simulations and phantom experiments are shown in Figs. mentclass2pt{minimpriori information about the number of targets but the proposed method still works. The inability of the implicit shape method reconstructing double targets with different fluorescent yields derives from that the level set function is unable to represent multiple targets unless these targets have the same fluorescent yield. If multiple regions can be recognized during the iterative process, the coefficient xf in Eq. (Figures f in Eq.  that desAs a variation of the Newton method, the LM method converges much faster than the gradient descent method which is a first order method as shown in Figs. Figures xb and xf, which results in the requirement of the priori information about the number of targets. On the contrary, the cosine function makes the fluorescent yield vary between xb and xf, hence the priori information about the number of targets is not required any more. However, the variable fluorescent yield also results in the blurring of the reconstructed shapes. This is the disadvantage of the cosine function.The difference between the proposed method and the implicit shape method derives from the replacement of the Heaviside function with the cosine function in Eq. . The priGenerally, the proposed method can be considered as a compromise between the image-based method and the implicit shape method. Taking advantage of the Newton-type method, the image-based method is good at fast convergence and stable reconstruction but suffers from low image clarity. On the contrary, the implicit shape method provides high image clarity with the level set function but suffers from a slow convergence speed and unstable reconstruction due to the utilization of first order methods. The proposed method implements both the Newton-type method and the level set function to achieve the advantages of both the two methods. However, the proposed method is incapable of obtaining images with explicit boundaries because the cosine function blurs the shapes of the reconstruction results.In conclusion, a shape-based reconstruction scheme of FMT with cosinoidal level set method is proposed in this paper. This reconstruction method replaces the Heaviside function with a cosine function in the classical implicit shape method so as to take use of the Levenberg–Marquardt method. The proposed method provides a faster convergence speed than the implicit shape method and higher image clarity than the image-based reconstruction method. Furthermore, the proposed method does not need to know the number of targets and avoids the choice of step length, which is an intractable problem in the gradient descent method. As a result, the proposed method performs more stably than the implicit shape method.


A computational model of cat auditory nerve fiber (ANF) responses to electrical stimulation is presented. The model assumes that (1) there exist at least two sites of spike generation along the ANF and (2) both an anodic (positive) and a cathodic (negative) charge in isolation can evoke a spike. A single ANF is modeled as a network of two exponential integrate-and-fire point-neuron models, referred to as peripheral and central axons of the ANF. The peripheral axon is excited by the cathodic charge, inhibited by the anodic charge, and exhibits longer spike latencies than the central axon; the central axon is excited by the anodic charge, inhibited by the cathodic charge, and exhibits shorter spike latencies than the peripheral axon. The model also includes subthreshold and suprathreshold adaptive feedback loops which continuously modify the membrane potential and can account for effects of facilitation, accommodation, refractoriness, and spike-rate adaptation in ANF. Although the model is parameterized using data for either single or paired pulse stimulation with monophasic rectangular pulses, it correctly predicts effects of various stimulus pulse shapes, stimulation pulse rates, and level on the neural response statistics. The model may serve as a framework to explore the effects of different stimulus parameters on psychophysical performance measured in cochlear implant listeners. Patients with severe hearing loss or deafness are commonly prescribed with cochlear implants (CIs). The CIs bypass the impaired mechano-electrical transduction pathway through the cochlea and directly stimulate the auditory nerve fibers (ANFs) with electric pulses. CI signal processing strategies aim to mimic the cochlear processing of the acoustic inputs and to provide the CI listeners the “essential” cues for successful communication. Primarily, they extract the slowly-varying envelopes of the acoustic signals and stimulate the ANFs with a train of biphasic pulses modulated with the processed envelope  describes the passive filtering of the stimulus along with the exponential upswing of the membrane potential during spike generation in the axon. The noise term INoise introduces stochasticity in the membrane voltage and is modeled as a random process with a Gaussian amplitude distribution and a power spectrum proportional to 1/fα, inspired by the recordings of stochasticity in neural membrane voltages (Verveen and Derksen where h(V), is described as the sum of a linear and an exponential function:The passive filtering of the stimulus in each axon, gL is the membrane conductance, EL is the resting membrane potential, ∆T represents the slope factor of the exponential function, and vthreshold is the threshold potential. In common integrate-and-fire models, a spike is indicated when the membrane potential crosses vthreshold. In the exponential integrate-and-fire model described in Eq. vthreshold. The increase of the membrane potential beyond vthreshold is exponential and the rate of the increase is determined by the slope factor ∆T. To indicate a spike discharge in this model, the peak voltage vpeak is introduced which indicates the membrane voltage at which the spike is generated. The corresponding time of spiking is denoted as tspike. After spiking, the membrane potential is reset to vreset.where Isub and Isupra are described in Eqs. The subthreshold and suprathreshold adaptive currents asub and asupra and the time constants of the subthreshold and suprathreshold adaptation V.with the conductances tspike. The spike triggers an adaptation process that modifies the suprathreshold adaptation current, described in Eq. b, which accounts for the spike-rate adaptation , in which I+(t) is the anodic (positive) charge and I−(t) is the cathodic (negative) charge. To allow the peripheral axon to be excited by a cathodic charge and inhibited by an anodic charge while using the same underlying equation, the input to the peripheral axon is the inverted temporal waveform of Istim(t). An additional parameter, β, is included in the model to vary the effect of the inhibitory phase on spike generation. When β equals 0, the inhibitory phase of the stimulus is fully removed and when β equals to 1, the inhibitory phase remains unchanged. As a result, the total input stimulus waveform to the two axons can be expressed as:The input to the model is a temporal waveform of the stimulus, IStim  represents the stimulus input entering the peripheral axon, IStim  represents the stimulus input entering the central axon, I− is the cathodic charge, I+ is the anodic charge and β is the scaling factor for the inhibitory charge. Both axons simultaneously receive the stimulus input and independently calculate the membrane potential at each location.where gL and C) and stochasticity of neural responses (INoise) were estimated from ANF responses to electrical stimulation with monophasic anodic and cathodic pulses in cats. The method used to estimate these parameters is described in the following paragraphs. The other remaining parameters of the model were estimated to best represent the responses to monophasic stimulation. The complete set of obtained values is presented in Table The model parameters that determine the charge integration properties of the neural membrane   y-intercθ and standard deviation σ. The mean (θ) specifies the stimulus level that evokes a neural response with a probability of 0.5 and is defined as the threshold for ANF spiking. Sigma (σ) is a measure of the stochasticity of the neuron’s response to a stimulus at a given level. A normalized measure that combines θ and σ, the relative spread (RS), is obtained by taking the ratio of the standard deviation to the threshold of the neuron spiking (σ/θ). RS values are often reported to describe the normalized dynamic range of the ANFs  function which reflects the probability of spiking as a function of the stimulus level Verveen . The FE r et al. .The effects of commonly used stimulus parameters, such as the pulse phase duration (PPD), interphase gap (IPG), stimulation pulse rate, and pulse level on the model responses were evaluated and compared to measured ANF responses. The response statistics from measured ANF responses were obtained by digitizing the individual data points from the corresponding studies. The stimulus conditions and the statistical measures to describe the neural responses were chosen to be identical with the respective studies in order to facilitate a comparison of the predictions with the data. The model was implemented in MATLAB . The differential equations of the model were solved using the forward Euler method with an integration time step of 1 μs. All simulations were run with a constant set of parameters shown in Table The considered pulse configurations for single pulses are illustrated in Figure In the present study, predictions were obtained for monophasic pulses with PPD of 25 to 500 μs of either anodic or cathodic polarity, and for biphasic pulses of either anodic or cathodic leading polarity with 25 μs to 10,000 μs PPD. The predicted response statistics for monophasic and biphasic pulses were compared with the data from Miller et al. , 2001b, the variable-probe condition. In the second paradigm, the conditioner and the probe are presented at the same level and with different relative delays  and a long-duration second phase (160 μs) of opposite polarity. In each condition, the conditioner and the probe were identical in their pulse shape. The conditioner and probe levels were kept constant at either +1 or +3 dB above the threshold for a single pulse and the interpulse delays were varied from 500 to 16,000 μs. The effects of the suprathreshold paired pulse stimulation were compared to the data from Dynes . The pulse trains were 300 ms in duration and composed of symmetric biphasic pulses of either anodic or cathodic leading polarity. The amplitudes of the pulses in a pulse train were constant and varied across conditions between −10 and +10 dB above the threshold for a single pulse. The predictions were compared to the data from Javel , Bruce eθ and standard deviation σ to obtain the FE function. The threshold was defined as the value of θ of the FE function. The dynamic range of the neuron was estimated by calculating the RS as σ/θ. The spike latency distribution was calculated from the time delays of the generated spikes relative to the stimulus onset. The standard deviation of the spike latency distribution was then defined as the spike jitter.For single and paired pulses, the response statistics used to characterize the neural response included threshold, dynamic range, spike latency, and jitter. First, the spike probabilities were obtained by repeating the simulations 1000 times at multiple current levels. The probabilities were fit with an integrated Gaussian function described with mean For pulse trains, the response can be described by the spike rate and its variability, the dynamic range, the interspike interval (ISI) histogram, and the vector strength (VS). The spike rate is defined as the observed number of spikes per second for any given stimulus at a particular stimulus level. The variability in spike rate can be quantified using the Fano factor. The Fano factor is a normalized measure of the variance in spike rate and can be described as the ratio of the standard deviation of the spike rate to the mean spike rate, evaluated across repetitions of the stimulus. The dynamic range of the neuron was derived by calculating the rate-level function via simulations of the spike rate at multiple levels. The ISI histogram was considered to represent information related to the temporal dispersion of the spike times and was constructed with a bin-width of 1 ms. The VS was calculated to quantify the periodicity in the neural responses. It represents the phase locking of the spike times in response to sinusoidal stimulation:N is the total number of spikes used in the analysis, ti is an individual spike time (in seconds), and T is a period of the sinusoid for which the synchronization of spike times is being assessed. The value of the VS can maximally be 1, indicating perfect phase locking, and minimally 0, indicating no phase locking to the stimulus frequency. In order to avoid any effect of the onset responses to the stimuli, the spikes appearing in the first 50 ms of the stimulus were excluded from the calculation of the VS. The effect of the pulse rate on the VS was obtained for the pulse train stimuli presented at a level of 1 dB above the threshold for a single pulse. The effect of level on the model responses was quantified by selecting stimulus levels which resulted in spikes rates from 4 to 500 spikes/s.where Changes in neural responses across time were investigated by constructing the peri-stimulus time histograms (PSTH) and wide-bin adaptive peri-stimulus time histograms (aPSTH) in response to pulse trains. The PSTH were constructed with a bin-width of 1 ms from responses to the pulse train stimuli presented at a level of 1 dB above the threshold for a single pulse. The aPSTH refers to the PSTH constructed with increasing time windows across the stimulus duration. Following Zhang et al. , the aPSmonophasic anodic and cathodic pulses of 26- and 39-μs duration are shown in Figure The simulated response statistics for The comparison of the predictions to data for 26- and 39-μs-long anodic and cathodic monophasic pulses is shown in Figure symmetric biphasic pulses. Figure Figure Figure Figure pseudomonophasic pulses as a function of the duration of the second, anodic phase (black line). The thresholds were normalized relative to the threshold for a symmetric biphasic pulse with 40 μs PPD. The threshold for a cathodic monophasic pulse of 40 μs is also shown on the right for comparison. The corresponding mean data from Miller et al. (2001) are indicated by the red circles, and standard deviation of the data is represented by the shaded area. Both predictions and data show that the thresholds decrease monotonically with increasing anodic phase duration. Thresholds continue to decrease beyond 1000 μs asymptotically approaching the threshold for a monophasic cathodic pulse. The predictions are in good agreement with the data.Figure subthreshold conditioner are shown in Figure The simulated response statistics for paired pulses with a In Figure suprathreshold conditioner are shown in Figure The predictions for paired pulse stimulation with pseudomonophasic pulses with a Figure The predictions for pulse train stimulation are shown in Figure Figure Figure Figures Figure Figure Figure In this study, a computational model of the ANF responses to electrical stimulation was presented. The structure of the model was motivated by the experimental observation that both anodic and cathodic charges can generate a spike, whereby the site of spike generation differs for the two polarities. The model assumes two independent point neurons which mimic two sites of spike generation, namely the peripheral and the central axons of the ANF. The differences in sensitivity for anodic and cathodic charges was introduced in the model through the parameters derived from the rheobase and the chronaxie for monophasic pulses, using a procedure which describes the strength-duration function as a linear function instead of the traditionally considered exponential function. The model was evaluated in stimulus conditions with single pulses of various pulse shapes as well as with paired pulses and pulse trains. The results demonstrate that the charge integration properties of the neural membrane derived from responses to monophasic pulses can characterize the responsiveness of the neuron to electrical stimulation sufficiently well to account for the stimulation with biphasic pulses and pulses of alternative shapes.The dynamic response properties of the ANF responses were modeled by two feedback current loops, describing the subthreshold and the suprathreshold currents which continuously modify the membrane voltage with respective time constants  instead of the white noise. The use of 1/fα shaped noise produces physiologically realistic fluctuations of the membrane voltage . In that framework, a spiking threshold is assumed to be random with a Gaussian distribution identical to that underlying the FE function and is approximated by white noise. In contrast, in the present study, the stochasticity is simulated as fluctuations in the membrane voltage using spectrally shaped noise  than the site of spike generation for a monophasic, cathodic pulse . The model was parametrized using limited data for monophasic stimulation, and model responses were compared to available data, mainly from electrically stimulated ANFs in cats. The model was shown to correctly account for stimulation with alternative pulse shapes as well as with dynamic stimuli such as pulse trains of different pulse rates and stimulus levels. Overall, the proposed model framework can serve as a useful tool to explore the temporal coding in the electrically stimulated ANF in response to various CI stimuli and to quantify potential benefits to the CI listeners.


A further restriction in most interferometric systems is for focusing the system on the measured object. We present two methods that overcome these restrictions. In the first method, different segments of a measured wavefront are digitally propagated and focused locally after measurement. The divergent distances, by which the diverse segments of the wavefront are propagated in order to achieve a focused image, provide enough information so as to resolve the 2π ambiguity. The second method employs an interferogram obtained by a spectrum constituting a small number of wavelengths. The magnitude of the interferogram's modulations is utilized to resolve the 2π ambiguity. Such methods of wavefront propagation enable several applications such as focusing and resolving the 2π ambiguity, as described in the article.Phase measurements obtained by high-coherence interferometry are restricted by the 2 In order to increase the dynamic range of 3D measurements for continuous objects, known unwrapping algorithms can be used [π ambiguity is resolved and a considerably larger dynamic range can be measured. In this article, we suggest to overcome this restriction regarding a step-like object by digitally propagating the measured wavefront reflected by the object and refocusing it. By focusing each segment of the wavefront locally and by retaining the distances by which each part of the wavefront was propagated and focused, the information as to resolve the 2π ambiguity is provided. Moreover, this procedure obviates the need for autofocusing mechanism simply by taking a measurement and propagating it to the image plane.Highly accurate phase measurements are very important in applications of surface measurements –3. Never be used , 5. Howe be used . By compA is the reflectance of the object and φ is the phase map of the reflected wavefront which is related to the height map h of the object. By approximation, the phase map φ is given byλ is the wavelength and mod 2π is the phase modulus of 2π. Accordingly, the height map of the object is restricted by the 2π ambiguity, and it can be reconstructed unambiguously from the phase map φ, provided that the pixel-to-pixel height differences are less than λ/2. Moreover, when focusing the interferometer on a certain plane ringing artifacts occur as a result of unfocused levels which influence focused planes. This effect, which is created due to the propagation of the wavefront and which belongs to the unfocused sections of the measured surface to the same level as the focused sections, is known as the Gibbs phenomenon. The ringing artifacts for a piston object with height differences of 108 μm are illustrated in λ = 0.5 μm reflected from the two height levels. The complex amplitude of a wavefront obtained by a uniformly collimated monochromatic beam of light reflected from an object is given byπ ambiguity. Moreover, due to the focusing problem, a distortion of ±15 nm is perceived on the border of the adjoining height levels. It is important to note that unwrapping is inefficient in this case. The variety of potential levels, complying with the condition of h = mλ/2, makes it impossible to deduce the real deviation.The gray levels and the reconstructed heights, of both the upper and lower segments of the surface, are identical due to the 2There are many existing autofocus methods, which are used for various types of optical devices. Most of them are based on sharpness function, which is a real-valued estimate of the image's sharpness . In mostAs part of the above presented methods, several “focusing criteria” have been adapted and developed by our team. These criteria define the wavefront of a focused image and are based on the changes in diffraction and Gibbs phenomena when a wavefront is propagated from a plane to another one.(i) The Fourier Transform Criterion. In this criterion [U is checked according to the integral of the absolute value of the Fourier Transform of the squared wavefront [riterion , the spaavefront :(3)CFFTU(ii) The Standard Deviation Criterion. This criterion checks the shape of the spatial wavefront behavior U as a function of the local standard deviation of the squared wavefront [σ represents the standard deviation operator. The assumption, on which this criterion is based, is as follows: since, for nonfocused image, the changes in the amplitude in the image are much stronger than for a focused image, the value of the overall standard deviation of the squared wavefront will be the smallest at the focused image.avefront :(4)CStdU(iii) The Gradient Criterion. Based on this criterion, the focusing level of the image is checked as a function of the local integral of the modulus of the local gradient of the square wavefront [avefront :(5)CGradhenomena , 12, are(iv) The Entropy Criterion. At the end, the last criterion is based on the previous one and is the local integral of the modulus of the gradient of the complex wavefront. This criterion takes also into account not only the intensity function as the abovementioned methods [ methods , 9 but a methods :(6)CEntUPz located at a distance z from the plane P positioned at z = 0 is [λ is the wavelength andɛ(z) = ±1 is the sign of z, and the symbol ∗ stands for convolution. For the plane waves' decomposition, the formula of wavefront propagation, known also as the “angular spectrum,” is given by [νx and νy are the spatial frequencies and F stands for the Fourier Transform. For both fzx,y=given by 9)fz=FF−fzx,y=givfz=FF−fzxμm and −400 μm. As a result the defocused image is blurred and possesses a greater amount of ripples which occur around edges, relative to the focused image.Figures μm. The added value of such an approach (The defocused wavefront was propagated by means of BPM program, towards the image plane while calculating the focus criteria values. In approach  is that π ambiguity when refocusing each segment of the wavefront locally. Once the wavefront has been measured for a certain plane P, each segment of the wavefront can be propagated to a certain plane at which the image has a minimum amount of ripples around edges. This plane can be defined as the image plane of that segment. The distance by which each part of the wavefront has been propagated provides the additional information for resolving the 2π ambiguity. We have measured the wavefront reflected from an object containing two segments, a substrate and a step height as shown in π ambiguity range. The measurements were taken with an imaging interferometer [λ/2, it can be combined with the interferometric measurements to resolve the 2π ambiguity. Accordingly, the interferometric measurement gives the most accurate result, while the digital wavefront propagation provides additional information for the solution of 2π ambiguities. It should be noted that this method requires some a priori knowledge about the configuration of the step-like object and a minimal number of pixels within each object's segment in order to obtain an unambiguous result.This technique can also be utilized for resolving the 2erometer , 11 mounπ ambiguity by measuring the object using two or more discreet wavelengths.Here we suggest another method  for resoπ ambiguity, the resolution is not so important.The object's heights are obtained in the same fashion as in noncoherent interferometry, by adding the interference patterns obtained by the different discreet wavelengths to obtain the interferogram and calculating the position of the centered maximum of the interferogram. The main advantage here is that, as opposed to noncoherent interferometry, there is no need for moving mirror to obtain the interferogram. Since the light for each wavelength is coherent, the measured wavefronts can be propagated electronically. It should be noted that using discreet number of wavelengths the interferogram is periodic and the resolution is limited. However, since this technique may be used only for resolving the 2λ1 = 720 nm, λ2 = 740 nm, and λ3 = 760 nm. An interferogram generated by propagating the three wavefronts is shown in We have simulated this technique by carefully selecting three wavelengths that will yield satisfactory results: λ. A small Δλ is preferable since closer wavelengths generate large periodic segments. We have checked the immunity of this method to noise by adding random noise to the interferograms as shown in At differing heights of the sample, the same interferogram initializes at distinct positions, allowing the retrieval of sample's shape. As illustrated above, the centered maximum value relocates itself linearly as a function of depth changes. Nevertheless, as perceived from the figure, amplitudes can coincide for two different levels, and, as a consequence, several multiples of the periodic cycle are exactly lying, one on each other. Truly, such confinement can be neglected. As for ranges of 15 to 55 microns it can be detected, depending on the opted wavelengths. For longer wavelengths this range increases, and therefore usage of infrared illumination is indicated. Another criterion influencing the periodic segment is ΔAccording to our results, even in presence of noise artifacts it is feasible to distinguish the precise position of each height according to the amplitude of intensity modulations. Moreover, it is well known that the usage of multiple wavelengths is sensitive to noise, especially for close wavelengths. Our method is not influenced by such noise since it seeks for a graph's maximum obtained as a result of multiple propagations and for a maxima obtained from the global propagation of each wavefront in each field of vision and not only for local results. So, even if there is any local concern, the global propagation enables its repair.π ambiguity in interferometric measurements. The first method consists in beam propagation of the measured wavefront. This method enables the extension of the dynamic range of single wavelength interferometry beyond the limitation of λ/2 even for step-like objects. The second technique utilizes several wavelengths in order to acquire a discrete wavelengths interferometry measurements as well as obtaining the interferograms simply by electronic propagating and adding the wavefronts without the need for moving the interferometer's mirror. Divergent sections of the interferogram represent differing heights, while each section undergoes different intensity modulations. We have demonstrated and implemented these methods, proving their promising usefulness. In addition to resolving the 2π ambiguity, these procedures obviate the need for focusing the interferometer on the measured object.In conclusion, we have introduced two new methods in order to resolve the 2


In evolutionary biomechanics it is often considered that gaits should evolve to minimize the energetic cost of travelling a given distance. In gait simulation this goal often leads to convincing gait generation. However, as the musculoskeletal models used get increasingly sophisticated, it becomes apparent that such a single goal can lead to extremely unrealistic gait patterns. In this paper, we explore the effects of requiring adequate lateral stability and show how this increases both energetic cost and the realism of the generated walking gait in a high biofidelity chimpanzee musculoskeletal model. We also explore the effects of changing the footfall sequences in the simulation so it mimics both the diagonal sequence walking gaits that primates typically use and also the lateral sequence walking gaits that are much more widespread among mammals. It is apparent that adding a lateral stability criterion has an important effect on the footfall phase relationship, suggesting that lateral stability may be one of the key drivers behind the observed footfall sequences in quadrupedal gaits. The observation that single optimization goals are no longer adequate for generating gait in current models has important implications for the use of biomimetic virtual robots to predict the locomotor patterns in fossil animals. However, while interest in these gaits can be traced back to the origins of dressage in the 16th century, we are still unable to categorically define why a particular animal would choose a particular gait at a particular speed ,3), althstability margin as the shortest distance from the vertical projection of the centre of gravity to the boundary of the support pattern. This value is positive when a gait is statically stable and becomes negative when the gait is dynamically stable, and can be used as a pragmatic metric for estimating the size of external perturbation that a gait can accommodate without losing the property of being statically stable [It is important to distinguish the various uses of the term ‘stability' in mechanics. In this paper, we are referring to stability in the orientation axes. In particular, we are interested in lateral stability which is the tendency for a moving body to recover from small roll perturbations and, therefore, move forward with relatively small oscillations about the longitudinal axis. This use of the term stability  is commonly encountered in aeronautics  but is ey stable . The advy stable . There ay stable , with asComputer simulations of quadrupedal locomotion are an important tool for investigating locomotion but these tend to be rather abstract models designed to answer particular aspects of the mechanics rather than providing a high level of realism ) of 0.25 because this is just over the minimum cost of transport speed (0.23) previously found [To test the effect of optimization goal and footfall patterns on the gait produced by the model, we created two sets of starting conditions. The first was based on chimpanzee kinematics recorded previously , which procedure , and a srocedure  to invesly found  and in tly found .loudDigitiser  through which the flank of the animal passed while walking on the platform . For the initial case starting from a random genome, most simulations did not produce a reliable gait that could progress forward a significant distance over multiple strides, so the best five were chosen from each starting condition that showed the desired gait characteristics in terms of footfall pattern . These were then further optimized using our standard procedure where each subsequent run uses a previous mid-simulation pose as its starting pose, and uses the best previous solution population as its starting solution [The simulations were run as a balanced two-factor design. Factor 1 was the starting condition . Factor 2 was the amount of lateral speed restriction  but not for footfall sequence. The restriction of lateral velocity to less than 0.2 m s−1 causes an 18% increase in cost of locomotion and restriction to less than 0.1 m s−1 causes a 32% increase on average, although there is quite a high degree of variation between individual values. Figure 5b shows the effects on the mean forward velocity. Again, ANOVA shows a statistically significant effect of the lateral velocity limit  with a 9% reduction for less than 0.2 m s−1 and 8% for less than 0.1 m s−1. This change is relatively small and may reflect the fact that the simulation's forward speed is also limited. The effects on gait cycle time are shown in figure 5c but no statistically significant effects were seen. Figure 5d shows the effects of the lateral velocity limit on the measured peak lateral velocity. As expected these limits have a major effect on the lateral velocity generated  but with no difference between the lateral and diagonal gaits. The peak lateral velocity seen when there is no limit is 47% of the mean forward velocity, suggesting relatively high levels of lateral movement are used in the simulation to maximize energy efficiency.Figure 5a,b show the effects on the fore and hind limb duty factors of the simulation. The only statistically significant effect here is a 13% increase in forelimb duty factor in the less than 0.2 m s−1 case . The effects on the phase relationships between the limbs are show in figure 6c,d. Figure 6c is the phase lag of the left hand contact as a proportion (0 to 1) of the gait cycle which starts with left foot contact. Thus, diagonal gaits  have values greater than 0.5, and lateral gaits  have values less than 0.5. This is clearly seen in figure 6c with the expected values for diagonal and lateral gaits seen depending on the start condition . There is also an effect of the lateral velocity limits which moderate the effect of the starting gait condition . What appears to be happening is that the lateral velocity constraint is forcing a greater degree of diagonality, and this is further explored in figure 6d which shows the phase difference from 0.5 with the sign removed. This removes the effect of the starting condition almost completely  and shows that the effect on both lateral and diagonal gaits in terms of increasing diagonality is largely identical . With the peak lateral velocity restricted to less than 0.1 m s−1 the difference from 0.5 is less than 5%, so this would generally be considered to be within the trotting phase space [The temporal characteristics of the generated gaits are further explored in Figure 6se space .Figure 4.−1 m−1 ranging between 2.8 and 5.8 [−1 O2 [−1 m−1 with no lateral stability constraint rising to 5.74 with the less than 0.2 m s−1 constraint and 6.39 with the less than 0.2 m s−1 constraint. This may explain why previous results have led to appreciable lateral movement because it would appear that there is a real energetic cost to maintaining a laterally stable stance, and an optimization strategy that is only looking for minimal energy cost would, therefore, not identify these solutions. We would suggest that this may be due to the model taking advantage of lateral sway pendulum mechanics for additional energy recovery as has been reported in penguins [−1  [The inclusion of a lateral stability requirement is certainly shown to improve the match between the simulated gait and the experimentally recorded gait in terms of lateral displacements. This is unsurprising because it applies an additional constraint to a model that already produces moderately convincing gait (certainly when viewed from the side). What is more interesting is the effect of this constraint on the other gait parameters in the simulated outcomes. There is a mean increase in the metabolic energy cost of locomotion of 18% for a moderate lateral stability requirement and a 32% increase for the more stringent case. The experimentally measured mean cost of locomotion for quadrupedally walking chimpanzees is 3.8 J kg and 5.8  . The sipenguins , howeverpenguins , so thatbration) , so the bration)  so thesebration) ).Pan paniscus produced very similar answers with phase lags in chimpanzees ranging fairly uniformly between 40% and 75% [The footfall picture is equally interesting. The simulation itself is equally adept at producing both lateral and diagonal gaits and our results show very little effect of footfall sequence on any of the measured gait parameters, even though their effects on velocity and locomotor costs are substantial. Duty factors mostly fall within the experimentally observed range (0.62–0.74 ). Hildeb and 75% . Clearly and 75% ) are muc and 75% , and it  and 75% . However and 75% ,53. Howe and 75%  and thatAll gait models are to some extent a simplification of reality, and the chimpanzee model presented here is no exception. Its main limitation in the context of the current work is probably the lack of mobility at the limb girdles and in the trunk itself. The latest quadrupedal robots consider trunk mobility as a key component (e.g. ) and the5.The realism of the gait produced by the chimpanzee model is considerably enhanced by including a lateral stability criterion and it is highly likely that this is an important evolutionary consideration. This enhanced lateral stability comes at a moderate energetic cost, however, and this cost would need to be outweighed by other adaptive advantages. The change in footfall phase relationships strongly supports arguments about the advantage of highly diagonal gaits in terms of lateral stability, but the current model does not help identify any functional advantage of diagonal over lateral gaits among primates.


Improvements in eddy current suppression are necessary to meet the demand for increasing miniaturization of inductively driven transmission systems in industrial and biomedical applications. The high magnetic permeability and the simultaneously low electrical conductivity of ferrite materials make them ideal candidates for shielding metallic surfaces. For systems like cochlear implants the transmission of data as well as energy over an inductive link is conducted within a well-defined parameter set. For these systems, the shielding can be of particular importance if the properties of the link can be preserved.In this work, we investigate the effect of single and double-layered substrates consisting of ferrite and/or copper on the inductance and coupling of planar spiral coils. The examined link systems represent realistic configurations for active implantable systems such as cochlear implants. Experimental measurements are complemented with analytical calculations and finite element simulations, which are in good agreement for all measured parameters. The results are then used to study the transfer efficiency of an inductive link in a series–parallel resonant topology as a function of substrate size, the number of coil turns and coil separation.We find that ferrite sheets can be used to shield the system from unwanted metallic surfaces and to retain the inductive link parameters of the unperturbed system, particularly its transfer efficiency. The required size of the ferrite plates is comparable to the size of the coils, which makes the setup suitable for practical implementations. Since the sizes and geometries chosen for the studied inductive links are comparable to those of cochlear implants, our conclusions apply in particular to these systems. Contactless inductive transmission systems are used in a broad field of applications where wires between transmitter and receiver modules are impractical. The concept is based on inductively coupled coils that allow the simultaneous transfer of power and information. Typical examples can be found, e.g., in non-contact battery chargers for modern cell phones  or electThere is a continuing trend towards miniaturization of industrial and biomedical applications that use inductive transmission systems. This implies that system components with metallic surfaces or metallic interconnections between such components have to be positioned in the vicinity of the coils. If these structures are exposed to the alternating magnetic field of the link, eddy currents are induced due to Faraday’s Law . These eA fundamental solution to this problem would be to keep metallic objects away from the inductive transmission system, which may not be possible in many cases due to size requirements. In particular, the system studied in this paper is very similar to the inductive transmission system of cochlear implants. Due to the compactness of present devices like single unit processors and prospective even more compact future designs, metallic structures such as the electronics of the speech processor, the microphone or the battery housed in metallic packages can be very close to the transmitter coil, calling for alternative solutions. One possibility is the insertion of a high-permeability ferrite plate between the coil and the conductive structures. The ferrite layer acts like a “magnetic mirror”, which deflects the magnetic flux occurring in the source coil from the conductive layer. This technique provides a shielding of the metallic object associated with a considerable reduction of the induced eddy currents.For a large variety of systems, the primary goal when using a ferrite layer is the shielding from electromagnetic field interferences . Since tFigure The present paper investigates the suitability of highly permeable ferrite plates for electromagnetic shielding of conductive structures in inductive transmission systems in the context of cochlear implants. We will show that ferrite sheets can be used in this context not only to restore the transfer efficiency of the unperturbed system but also the coil inductivities, coupling strength and consequently the resonance frequencies. A central question is also whether or not the size of ferrite plates for effective shielding can be kept in the same range as the size of the coils. These are prerequisites for already implemented systems to function despite a possible detrimental influence of metallic surfaces close to the link.The paper is organized as follows. In section “Air: The original air-cored coil system without substrate serves as a reference.Cop: The substrate consists of a single layer of copper. This configuration allows the unwanted influence of a conducting material near the link.Fer + Cop: The double-layered substrate, with the first layer consisting of ferrite, the second layer of copper. The ferrite sheet is placed between the primary coil and the copper plate and is in direct contact with the conductor in order to keep the magnetic field away from the copper layer  and the distance da (db) above the substrate. The two-layer substrate consists of a ferrite and a copper sheet and is characterized by the relative permeabilities A three-dimensional and a cross-sectional view of the setup reduced to two turns i at z = da is assumed to carry a harmonic current ω. With the mutual impedance Zij between the source turn i at z = da and the turn j at z = db we find the induced voltage Zij can be written asMij is the mutual inductance of an air-cored system without the substrate. The contribution to the impedance due to the substrate is denoted by the complex-valued parameter The turn ij=Zij·I . Accordiij=Zij·I , the mute model   the paraS, Q and λ can be found in  [S and Q depend solely on the geometry of the two turns, whereas the complex-valued parameter function λ also depends on the angular frequency ω.The full expressions for ound in  . The reai = j so that ha = hb and da = db. Consequently, the exponential term in Eq. (Mi=j in air no longer depends on da. For a detailed description we again refer to  [Equations  and 3)  3) can aentclass1pt{minimaefer to  .Na and Nb turns, respectively, on a double-layer substrate as shown in Fig. Za of coil a can be calculated as the sum of all mutual impedance pairs of coil a [As a next step, we consider the general case of two multiple-turn coils with f coil a  4\documeZi=j of all single turns, the second term accounts for the mutual impedances La of the coil asThe first term on the right hand side of Eq.  represenFrom Eq.  we can dLb is carried out analogously. The total impedance Zab between primary coil a and secondary coil b is obtained as the sum of all mutual impedances Zij,The calculation for the secondary coil inductance Mab can be obtained from the imaginary part of Zab asThe mutual inductance La, Lb and Mab allows us to compute the coupling coefficient k between the two coils of the inductive link viaHaving found analytical expressions for Z,ijSub in Eq. , the term j in Eq.  disappeaj in Eq. .Equations  and 3)  3) have FEM simulations have been performed in ANSYS 11.0. . For the simulations the spiral-shaped coils are replaced with sets of circular windings and rectangular profiles as has been done in the analytical model. This arrangement is rotationally symmetrical and consequently the three-dimensional simulation of the model can be replaced by the analysis of a two-dimensional cross section which fully reflects the 3D setup. With the same number of grid points, the reduction from the 3D to the 2D model allows for a much denser mesh grid at the same computational cost.An advantage of the ANSYS software is that the simulation geometry can be connected with active and passive discrete components, such as current and voltage sources, resistors and capacitors. In this way it is possible to implement complete inductive transmission networks relatively easily as will be shown in the “d = db − da. The substrate is fixed on top of a thin insulating foil which is placed on the primary coil, so that da is fixed to da = 0.14 mm, and db varies from about 3–10 mm for different setups. This covers the typical coil separations found in real cochlear implant systems. The two coils are identical with respect to the geometric parameters outer radius, pitch, width and thickness. The number of turns is fixed to Nb = 3 for the secondary coil, whereas Na for the primary coil varies between 1 and 24 in different measurements. The unperturbed air-cored system which serves as a reference operates at 11.7 MHz and has Na = 8 t with an inductance of L0 = 2.53 µH and an outer coil radius rcoil = 14.3 mm. The substrate is single or double-layered and consists of disc-shaped ferrite and copper sheets. In case of a double-layered substrate, we use matching substrate radii rsub, the optimal value for rsub will be determined in the subsequent section. The ferrite material used for shielding was IRLG5, a flexible ferrite foil from TDK  with a thickness of 0.5 mm. A 0.2 mm thick copper disc was used to simulate the metallic surface. For the experiments, printed circuit board (PCB) spiral coils were used. The turns are uniformly distributed, i.e. with constant pitch between the turns, starting from the outer coil radius.In addition to the analytical model and the FEM simulations, the different link configurations were analyzed in experimental setups. In Fig. To study the properties of the different link configurations we use measurements of the self- and mutual inductances and the coupling strength of the link. The setup for the measurements is shown in the bottom plot of Fig. La and Lb, the mutual inductance Mab and the coupling strength k are studied as a function of the coil separation d, both, for the inductive link on the double-layered substrate  and the original air-cored link. In the last subsection we study the transfer parameters for a transmission system in a practical biomedical implementation.In this section we will quantify the influence of single or double-layered substrates on the inductive link properties. In the following two subsections the self-inductance of the primary coil is studied as a function of the substrate radius and the number of coils, respectively. We show that a reduction of the number of turns together with the use of a sufficiently large ferrite sheet allows to closely match the inductance of the unperturbed air-cored system. We make use of these findings in the subsequent subsection, where the primary and secondary inductances La as a function of the substrate radius rsub. The objective of this measurement is to find the minimal value of rsub so that the link can still be sufficiently shielded from the perturbing conductor and yields a high level of compliance with the analytical model which is based on an infinite substrate. For reference we here also study a setup with a single-layer ferrite substrate (Fer) which should show a similar behaviour as the combined Fer + Cop setup for larger substrate radii. The number of turns of the primary coil is fixed to Na = 8 in this configuration.We study the influence of the substrate in the three configurations Air, Cop, Fer + Cop, as described at the beginning of the section “rsub = 0 all results approach the value of the air-cored system (shown in blue), except the analytical model which always assumes an infinite substrate. A single layer of copper (red lines and markers) near the link leads to a reduction of the self-inductance with increasing substrate radius, due to the induced eddy currents, which levels off at about rsub = rcoil. In contrast, a single-layered ferrite foil (shown in green) results in a significant increase of the initial value. Dependent on the relative permeability and the substrate thickness a theoretical enhancement of up to 100 % compared to the corresponding value of the air-cored system can be obtained  [In Fig. btained  . The ferL0 for a substrate radius rcoil the inductance is larger than in the air-cored case. For partly covered coils, the magnetic field is not fully reflected by the ferrite and thus the part of the field which bypasses the substrate induces eddy currents on the back side of the copper disc which results in a reduction of the inductance. An interesting aspect of the interplay of attenuation and enhancement of the inductivity is the resulting formation of an inductance well, in our setup at approximately 0.7 rcoil. The results show a very good agreement between experimental data, FEM simulations and the analytical model predictions, particularly for large substrate radii.The inductance for a double-layered substrate consisting of ferrite and copper . The very good agreement of the results for the double-layered substrate (green) with the reference air-cored setup (black) confirms that the ferrite layer provides an adequate shielding of the copper sheet and that the original system can be reproduced very well with the chosen substrate radius and the reduction in the number of turns.The values of the inductances g to Eq. . Figure Figures In the preceding sections we have shown that a ferrite shield is capable of countervailing the reduction in inductances and coupling strength caused by a metallic surface close to an inductive link. In the following we will analyze a practical implementation of a complete inductive transmission system as used in real systems like cochlea implants. We will show that the use of a ferrite shield does not significantly deteriorate the characteristic transfer parameters for practical implementations of the complete inductive transmission system compared to an equivalent air-cored coil system.Ca and La characterize the series resonant circuit, Cb and Lb form the parallel resonant circuit. The resistance RL is the combination of the occurring loads. In our setup we used Ca = 81 pF, Cb = 275 pF and RL = 620 Ω which are parameters typically used in the field of cochlea implants. The coils themselves are approximated by their equivalent series circuits, where Rsa and Rsb characterize the series resistances of primary and receiver coils, respectively. The values of the series resistors of the coils are frequency-dependent and their values Rsa(f) and Rsb(f) are shown in Fig. Our implementation of the inductive transmission system has a series–parallel topology as shown in Fig. η and the voltage gain ν, the inductive link is modelled by its T-equivalent circuit, as shown in Fig. For the calculation of the power transfer efficiency The expressions for the Z-parameters are given in Appendix η as a function of the coil separation d. The significant drop in both transfer parameters ν and η for the case of a copper substrate (red) shows the importance of an efficient shielding against an unwanted influence of conducting media close to an inductive link. The results for the double-layer substrate configuration Fer + Cop (green lines and markers) are very close to the respective results of the air-cored reference setup. This proves the capability of the ferrite foils to restore the efficiency of an inductive transmission system. Again, the analytical results are in good agreement with those obtained by experiment and FEM simulation, especially for small coil separations. As can be seen from Fig. Na = 8 is close to the value for a copper substrate and Na = 8 at the operating frequency of 11.7 MHz. Thus, the significant deterioration of the transfer characteristics of the inductive transmission system cannot be explained by the drop of the resistance alone but suggests that it is mainly caused by the drop in coupling due to the copper sheet. As the results demonstrate, this shortcoming can be eliminated almost completely by a ferrite shield.The values from the analytical model, the FEM simulations and the experimental measurements have been used to calculate the voltage gain and the power transfer efficiency via Eqs.  and 10)10). In FIn this paper we have analyzed the suitability of ferrite sheets as a shield of inductive transmission systems against the influence of metallic surfaces. In particular, we investigated the influence of single or double-layered substrates made of ferrite and/or copper on the link parameters, such as self-inductance and coupling. All results were obtained theoretically with a detailed analytical model as well as with FEM simulations and in addition were confirmed experimentally. The measurements show that copper-covered coils in inductive link systems lead to a significant drop of the self-inductance and coupling due to induced eddy current losses. We could demonstrate that a high shielding performance can be achieved by placing a finite ferrite plate between the coil and the copper disc. In this way, a setup with the same coil configuration leads to even higher values of the primary inductance for the double-layer configuration than for the air-cored reference system. The original link parameters such as inductances and coupling and hence the transfer efficiency can be retained through a reduction in the number of turns. Furthermore, we have shown that the shielding can be achieved for relatively small radii of the ferrite foil in the same order of magnitude as the coil radius which makes them a promising candidate for practical implementations. Our results are particularly relevant for cochlear implant systems, since coil dimensions in these systems closely match the ones we used in our examinations.η and for the voltage link gain ν are comparable to the values of the air-cored coil system. In all our investigations we found the measurements to be in good agreement with the calculations based on the analytical model and with FEM simulations. This good agreement shows that simulations and analytical calculations are a good possibility to describe transmission systems on various substrate configurations without having to carry out the sometimes cumbersome experiments.As a next step we investigated the transfer parameters for a transmission system in a practical biomedical implementation, where the coils are parts of a transmitter and receiver resonant circuit. In this case, our analysis shows that a copper substrate mimicking a detrimental conductor near an inductive transmission system leads to a massive drop in power transfer efficiency and voltage gain. The results demonstrate that the ferrite layer ensures excellent shielding from the unwanted influence of the copper sheet. The obtained values for the power transfer efficiency


Measurements of the diffuse spectral reflectance are usually not made as direct measurement of the incident and the reflected radiant flux but rather as measurements relative to a standard of known reflectance value.Goniophotometric methods, also called Indicatrix methods or point-by-point methods.Methods based on the Kubelka-Munk theory.Integrating sphere methods according to Taylor, Benford, Sharp-Little, van den Akker, Korte.For the calibration of such standards, different methods have been described in the literature:Various materials such as magnesium oxide, barium sulfate or opal glass are being used as standards. Their suitability as transfer or as working standards will be discussed.The results of comparative measurements between some of these methods will be given. Measurements of the diffuse spectral reflectance have been used for many years as a tool in the measurement of color .1 HoweveIt is the purpose of this paper to outline some of the most important methods for such calibrations, to discuss briefly the physical properties of various materials which are used as standards, and to present a few intercomparative data. In presenting the various methods only the main features will be given and those characteristics which are important for distinguishing the methods and the quantities which are measured. Giving the full theory for each method and all experimental details is beyond the frame of this paper and it must be left to the reader to study the details in the original references.Goniophotometric measurements of the reflectance indicatrix with numerical integration.Methods based on the Kubelka-Munk theory.Methods using integrating spheres.Although examples for all three groups will be given the emphasis will be on methods in the last group which has many interesting varieties and is most widely used.There are essentially three groups of methods for absolute reflectance measurements:The terms radiance and luminance are being used interchangeably. Luminance is used mainly where photometric measurements are involved, while radiance is used in the context of spectral measurements. Geometrically these terms are identical, however luminance refers to values measured with a detector whose spectral sensitivity distribution agrees with the CIE photometric standard observer function.d/d)diffuse/diffuse (/d)normal/diffuse (0d/0).diffuse/normal  and the reflected radiation is measured at various angles (angle of observation 0°≤ ϵ2≤90o) and various azimuths. The incident flux ϕ0 is determined by measuring either the intensity of the source [rϕ is determined by numerically integrating the measured goniometric values of the radiance [This method is also called the “indicatrix-method” or “point-by-point method.” The sample is irradiated with a narrow beam usually in the direction of or near the normal  where T is the measured transmittance) is a linear function of the thickness X. The ordinate intercept of this line is related to the reflectance of an infinite layer of the material.A different approach was taken by Butler  who was Law and Norris  used mea4 powder with Fe2O3 powder in known concentrations and showed that from these concentrations and the relative reflectances measured for each concentration the absolute reflectance of the standard used for the relative reflectance measurements could be determined. For a pure BaSO4 he found values very close to those published elsewhere. However, the method is timeconsuming and it was estimated that the determination of the reflectance “should be good to 0.5 percent” which is a poorer level of accuracy than can be achieved by other methods.The third method was proposed by Lindberg  who “dilIt appears that only the last of these three methods was developed specifically for the calibration of reflectance standards. It was attempted to achieve this with instrumentation which is standard equipment in an analytical laboratory: a spectrophotometer with a reflectance attachment and a weight scale.Interesting as these methods are their complexity and lack of accuracy and the fact that they are not immediately applicable to all types of reflectance standards seem to have precluded these methods from being adopted by major standardizing laboratories for the calibration of reflectance standards.In 1912 Nutting  publisheBased on certain considerations developed during the construction of an 88 inch integrating sphere for luminous flux measurements , A. H. TThe integrating sphere, see B0 is measured.The sample port remains open or is covered with a nonreflecting sample. A luminance B is measured.The sample port is covered with a sample having the same paint as the sphere wall. A luminance From the measured ratio k=B/B0 and the known geometrical constants of the sphere (diameter of sphere and sample port) the diffuse-diffuse reflectance wρ (“m” in Taylor’s eq 9) is calculated. For the determination of the reflectance ρx of an arbitrary sample the sample port is covered with this sample and a luminance Bx of the sphere wall is measured. From the ratio x = Bx/Bk0  the geometrical sphere constants, and wρ, the reflectance xρ is calculated.For the determination of the reflectance of the sphere wall two measurements are madeThis method obviously yields the diffuse/diffuse reflectance of sphere paint and sample. It is necessary to determine the reflectance of the sphere paint, before that of a sample can be determined. In Taylor’s theory the apertures for photometer and entering beam are considered negligibly small. Preston  and Middwρ of the sphere paint is determined as in the first Taylor method. Then the source L is mounted at the entrance port C, see B' is measured on the sphere wall. Then the unknown sample is mounted at the sample port and the luminance xB is measured. From the ratio x/B'R=B, the geometrical sphere constants, and wρ, the reflectance xρ is calculated (Taylor’s Eq 16).In this method the reflectance d/d reflectance of the sphere paint is determined in the first step but in the second step the 0/d reflectance of the flat sphere paint sample is compared with that of the unknown sample. The assumption is that d/d=ρρ0/d for the sphere paint which is only true if the paint is very matte and opaque.In this method the Taylor describes this method as follows: “the sample was placed in a sphere and a very narrow beam of light was projected through a small hole in the sphere wall onto the sphere surface at a point unscreened from the observation window, then onto the sample so placed that none of the first reflected light from it could reach the observation window. The ratio of the brightness of the window in the second case to that in the first case is the reflection factor of the test surface.”ϕ0 irradiates the sphere wall and the observation window receives radiation directly from the irradiated area as well as by multiple reflection from the sphere. Then the source is moved around to irradiate the sample S. The observation window receives only radiation by multiple reflection. The ratio of the two irradiances at the window is the 0/d reflectance of the sample.Taylor gives no drawings for this method but The essential feature of this method is the introduction of the screen B which blocks the observation window from receiving radiation from the irradiated spot on the sample. It is important to note that in this method it is not necessary to determine first the reflectance of the sphere paint. The measured ratio is not that of sample reflectance to sphere wall reflectance but rather the absolute reflectance of the sample itself.For this method, Taylor constructed a simple instrument which is described in reference 28. The influence of the apertures and the goniophotometric properties of the sphere paint were investigated by Reule .It must be mentioned that in the literature the terms “Taylor Method” or “Taylor Sphere” are often used without a clear indication which of the three methods is meant.a1=A1/4πr2 and a2= A2/4πr2 are obtained and if the two luminances or irradiances of the wall measured in the two fractional spheres are R1 and R2, the amount of radiation entering the spheres being identical, then it can be shown that the reflectance of the sphere wall is given by the simple relationd/d reflectance of the material. It has a strong resemblance to the first part of the first Taylor method for the determination of the reflectance of the sphere paint. However in Taylor’s method the removable portion of the sphere is flat and this makes Taylor’s theoretical considerations and the final equation rather complicated. In Benford’s method all removable sections are spherical and the theory and final equation are simple.Also in 1920 F. A. Benford published a paper  on an inIn two subsequent papers , 31 exteϕ0 enters the sphere and forms an irradiated spot at the wall from which flux ϕ′0 is reflected. The sample S receives only indirect irradiation from the sphere wall due to multiple reflections because of the screen B while all other areas of the wall receive direct illumination from ϕ′0 as well as the indirect radiation. The photometer P measures first the luminance sB of the sample and then the luminance wB of the unscreened sphere wall; the d/0 reflectance xρ of the sample is given by x =BS/Bw.ρThe third paper on integrating sphere methods published in 1920 was that by Sharp and Little . This meHere again the essential part is the baffle B which prevents the direct illumination of the sample from the irradiated area (which may be considered a secondary source within the sphere).The authors assumed that the apertures for the entering flux and for the photometer were negligibly small. Budde  expanded1 into lens L2 which in turn images the aperture F1 onto the sphere wall. The baffle near the center of the sphere blocks any direct radiation from the image (the secondary source within the sphere) to the sample. The “Filter” is one of a set of interference filters in a filter wheel to allow spectral measurements. A photometer system, consisting of lens L3, aperture F2, an opal glass and a photomultiplier, measures the radiance of the sample sB and then swings around to measure the radiance wB of the sphere wall. It can be shown thatA0=4πr2 = total sphere area, A1 = area of sample port and A2 = area of remaining sphere wall. The factor A0/(A1+A2) represents a correction factor for the entrance aperture and the two observation apertures which are supposed to be black. In this set-up the instrument yields the diffuse/normal reflectance factor according to the Sharp-Little method. It may be easily converted to the inverse geometry by exchanging the source (with lens L1) and the detector . Then it yields the normal/diffuse reflectance according to the third Taylor method.The schematic diagram of an instrument  which maThis instrument has been constructed at the National Research Council of Canada and is being used for the calibration of reflectance standards .p and the ratio of the reflectance of the auxiliary sphere to that of the flat sample (the ratio measured by the spectrophotometer) is r then it is shown that the diffuse/diffuse reflectance of the sphere paint, and the flat sample, is given by:In 1966 van den Akker et al.  publishel et al. , and thiThis method is presently used at the NBS for the calibration of reflectance standards.sL of the sample observed through window V1 to the radiance L of the illuminating hemisphere observed through window V2 gives the reflectance factor d/β0s/L=L of the sample which in this case for a matte sample is equal to the reflectance, ρ0/d.While in all previous methods the samples were mounted at a port of the integrating sphere Korte  describeThe most important property of the instrumental arrangement is the uniformity of the radiance of the irradiating hemisphere. Korte reports that a test was made on this uniformity and that it was better than 0.1 percent. The irradiating hemisphere has an aperture for the photometer. A correction for this aperture, which is a nonirradiating area, must be made.Erb  modifiedThis method was already described in principle by de la Perelle . Howeverρ=1.0) in a perfectly diffuse or Lambertian manner so that its radiance (luminance) is constant for all angles of viewing or that its radiant (luminous) intensity varies with the cosine of the angle between the normal and the angle of viewing. This theoretical concept will probably never be realized materially but the techniques for the measurement of absolute reflectances provide the calibration of material standards relative to this primary standard.The “primary” standard of reflectance is the perfect reflecting diffuser which reflects all incident radiation  or long term (months or years).Cleanability: the cleaning of a standard may be necessary, particularly in industrial use, and should not change its reflectance.Transportability: a standard may be required to be mechanically stable and rugged enough to be sent by mail.Absence of: fluorescence, hygroscopic effects, thermochromic and photochromic effects.Spectral nonselectivity: it may be necessary to have a spectrally nonselective standard.Considering the application or use of reflectance standards two major categories must be distinguished:“Transfer Standards” which are used to transfer a calibration  from one instrument to another, for example, from an absolute reflectometer to a commercial instrument for relative measurements.“Instrument Standards” which are used as day-to-day “working standards” in a particular instrument or as “master standards” for the periodical checking of a working standard. Ideally instrument standards are calibrated against a transfer standard in the instrument in which they are to be used.The selection of a material for calibration as a secondary reflectance standard must take into account not only the physical properties but also the application. The most important physical properties to be considered areThe requirements with respect to most of the above listed physical properties are rather obvious for both categories of standards. However there are some significant differences which must be clearly understood.Transfer standards which are exchanged between a laboratory with instrumentation for absolute reflectance measurements and a laboratory with an instrument for relative measurements, must be insensitive to differences in the geometric conditions, that is they should maintain their reflectance value.d/0 geometry should be calibrated in an absolute reflectometer with the same geometry. However, differences may exist in the diameter of the sphere, the existence or location of a gloss trap, the locations of detector aperture, screens, etc., and the transfer standard should be insensitive to them. This insensitivity to geometric differences requires that the standard be very matte, highly opaque and uniform. These are the most important characteristics of a transfer standard and the accuracy of a calibration will depend mostly on the conformity with these requirements.Obviously a standard for an instrument with a 4 plates [4 paint [4 tablets are so indifferent against changes in geometry that βd/0= ρ0d/=βd/8= ρ8/d [Materials which approximate the ideal matte surface together with high opacity and uniformity are: pressed BaSO4 plates , which a4 plates  are Lamb4 plates  with a m[4 paint , 49 and [4 paint  may be u/8= ρ8/d , 43.For instrument standards the major requirements are: long term stability and cleanability. The latter property is often achieved by giving the material a glossy surface which is much less liable to collect dirt and easier to clean than a matte surface. Examples of such instrument standards are Vitrolite,The differences in the requirements for both categories of standards cannot be emphasized enough. Translucent or glossy standards (such as Vitrolite) should never be used as transfer standards and even a change in the geometry within one instrument such as the introduction of a gloss trap necessitates the recalibration of the instrument standard if it is not matte and opaque.Various properties of materials, particularly the stability, have been discussed in a paper by Erb .Effects of polarization on the reflectance of materials for standardization purposes have recently been investigated –48, and 4 and other reflectance standard materials or sphere paints was also discussed in a paper by Grum and Luckey [The stability of BaSOd Luckey .4, MgO, etc.) the reflectance of the compacts decreased with increasing pressure.”The effect of pressure in the preparation of pressed tablets was investigated by Schatz  who concA polished surface of this material seems to be adequate as a working standard. A depolished, matte surface may be used as transfer standard only for short periods. Cleaning such a matte surface is very difficult and requires a carefully established cleaning procedure in order to yield repeatable values.The material is fluorescent if irradiated by radiation below 370 nm. This fluorescence appears as a faint orange general emission with occasional limited areas of considerably stronger orange emission. This clearly indicates some non-uniformity in the material which may be seen under grazing angles on a polished surface as a very faint difference in the surface texture. Consequently the material should be inspected for these inhomogeneities under fluorescent light and it should not be used in the UV.Some remarks are necessary on the Russian opal glass MS–20 which has been proposed for calibration purposes:A new material “Halon,” which is a fluorocarbon, has been recently proposed by Grum . However4 and their properties was given by Budde in 1960 [4 and several integrating sphere paints was recently prepared by Erb [A survey and discussion of reflectance values of smoked MgO and of BaSO in 1960 . A very d by Erb . A repord by Erb .LCE, Belgium PTB, Germany ETL, Japan VNIIM, USSR IEN, Italy Goniophotometric methods used atSharp-Little method  used at Double sphere method , 37 usedKorte-method , 54 used4) reported. Otherwise Taylor [Data which allow a comparison between goniophotometric and integrating sphere methods are difficult to find. Only in reference 55 are direct comparisons of measurements made in various laboratories on one material . Two of these 4 samples were hand-carried to PTB- Germany for measurements according to the Korte method and two were measured at NRC, Canada, according to the Sharp-Little method. The results are given in A direct comparison without such sample differences between the Korte-method and the Sharp- Little-method as modified by Budde  was arradβ/0 is equal to a reflectance dρ/0 which has the same value as the inverse reflectance ρ0/d. It must be emphasized that this simplification is not generally permissible and that its applicability must be investigated. Only for very matte and opaque samples is such simplification permissible. Pressed BaSO4 seems to be such a substance [At several stages in the preceding sections the simplifying assumption was made that the reflectance factor ubstance  and alsoWith respect to precision and accuracy of reflectance calibrations it is found that a precision of ±0.002 is possible whereas accuracies in the order of ±0.003 are claimed. However the discrepancies between values obtained in the double sphere method on one side or in the Sharp, Little and Korte-method on the other side are larger than these claimed accuracies and therefore only after these discrepancies have been explained can a more general statement on accuracy be made.The question may be asked why absolute measurements have been made mainly in national standardizing institutes and why instrument makers have generally refrained from making instruments which yield absolute values. The answer to this question is that absolute reflectance measurements, in spite of the apparent simplicity of the integrating sphere methods, are complex and accident prone. The design of an absolute reflectometer requires a complete understanding of the parameters wdiich may affect the measurements. And to maintain an absolute reflectometer in perfect working order is often beyond the capabilities of an industrial testing laboratory. The International Organization for Standardization (ISO) has recognized this situation with its efforts to establish international agreement in reflectance measurements by delegating the calibration of transfer standards to a few recognized laboratories and recommending only relative measurements throughout the international paper industry . PrelimiBasically this procedure is used with many measured quantities such as resistance voltage, weight, etc., where standardizing laboratories provide the absolute calibration of standards while in industry only measurements relative to those standards are made. There are many good reasons for applying this procedure also to the complicated field of reflectance measurements.