Determination of the glass wall effect in optical ... - OSA Publishing

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Research Article

Vol. 54, No. 13 / May 1 2015 / Applied Optics

Determination of the glass wall effect in optical measurement of temperature in liquid using Mach–Zehnder interferometer AMIRHOSSEIN AHADI*

AND

M. ZIAD SAGHIR

1

Ryerson University, Toronto, Ontario M5B2K3, Canada *Corresponding author: [email protected] Received 9 December 2014; revised 14 March 2015; accepted 16 March 2015; posted 17 March 2015 (Doc. ID 229359); published 22 April 2015

For optical experiments in which the change of refractive index is monitored, the refractive index of glass would change due to the change of temperature along the walls, and, as a result, the measurements of temperature and concentration would be affected. Because of this, one may use another temperature measurement technique parallel with a Mach–Zehnder interferometer (MZI). For instance, thermocouples or thermometers can be implemented inside the walls to obtain the temperature at the walls and close to the liquid region. The main limitation of this technique is that it provides information at a specific location and not along the walls or inside the liquid zone. On the other hand, the measurement is performed at the location close to the liquid region and not inside the liquid. Thus, in this study, we suggest using the optical method with some modifications that clear up the mentioned limitations. Accordingly, the optical effect of glass in the laser interferometry experiment is first studied. Then, we suggest two experimental methods based on modifications in the experimental setup and the image processing technique of MZI to accurately determine the glass effect and remove this effect from the temperature and concentration measurements. Implementing any of these techniques results in accurate measurement of the temperature and concentration of the liquid in any rectangular cell. Finally, according to the results of this study, it can be claimed that a temperature profile can be obtained precisely using MZI, and the existence of other apparatus to measure the temperature is redundant for the MZI setup. This outcome offers a simpler and more precise measurement of either temperature or concentration profiles of any transparent liquid. © 2015 Optical Society of America OCIS codes: (130.2755) Glass waveguides; (120.6780) Temperature; (120.6810) Thermal effects; (100.2650) Fringe analysis; (100.0100) Image processing; (120.3180) Interferometry. http://dx.doi.org/10.1364/AO.54.000D74

1. INTRODUCTION Mach–Zehnder interferometry is widely used for optical measurement of the refractive index change along the laser beam for a transparent fluid [1,2]. The change of the refractive index during different conditions can be interpreted as the change of temperature or concentration in the domain [2–5]. It has been repeatedly claimed that optical methods have the advantage of nonintrusiveness and high accuracy measurement [6–8]; thus, they are being used for different applications, and their usage has remarkably increased; furthermore, qualitative and quantitative data can be obtained from optical methods. On the other hand, there are limitations with the optical methods. First, the transparent media should be transparent. This either causes the application of this method for fully transparent fluids or a thin layer of unclear fluid [5,9,10] such as nanofluids with the high initial mass fraction of a nanoparticle [11].

The other restriction of these optical techniques refers to the usage of a transparent container to keep the domain at rest during the experiment. In particular, for the optical method in this study (MZI), the laser beam has to travel through the medium, and, as result, it creates a path through the container. If the index of refraction of the container does not change during the experiment because of any external sources, the effect of the container would be negligible. However, in most of the experimental cases, the main source that causes change of refraction in the media (such as change in temperature) causes the change of refraction in the container. One of the main applications of the MZI is to study the heat and mass transfer in the gas or liquid mixtures. Thermodiffusion is a coupled heat and mass transfer phenomenon that can be measured by strength of the separation of components of a specific mixture at the presence of temperature

1559-128X/15/130D74-08$15/0$15.00 © 2015 Optical Society of America

Research Article difference [12–14]. Many studies have used the MZI technique to measure thermodiffusion or diffusion coefficients in binary or ternary mixtures [5,15–17]. During this experiment, the change of concentration is not affected by the refractive index of the container (or glass walls). However, the change of temperature along the cell (essential condition for thermodiffusion phenomenon) results in the change of refractive index in the walls, which are located in between the cold and the hot sides. Because of this effect, most experimentalists have relied on other temperature measurement techniques than the optical one. Then they used the MZI results to analyze the mass transfer in the domain [10–19]. Accordingly, few thermocouples have been located across the cell to measure the temperature variation applied by Peltier elements [1]. On the other hand, there are few studies that have compared the temperature measurement using the optical method and the thermocouples [1,2,4,5]. These investigations observed that there were some small transient fluctuations in the temperature profile (>0.4 K) across the cell. The observed fluctuations were not controlled or detected using the thermocouple sensors. The experimentalist have used two various approaches to address the effect of the wall glass in their measurement. The first approach is using the specific material in which the optical properties do not have strong dependency to the temperature variation. In these cases, the optical impact of the small change of temperature across the walls would not cause a noticeable change in the final optical result. The second approach to address the optical impact of the wall was to introduce an error bar to the optical measurement values in which the error bar can be calculated based on the temperature refractive index of the walls material. It can be seen that, in both approaches, no accurate determination of the impact of the glass was employed. Thus, measurement of the temperature using the optical method in these studies has been questioned with respect to the glass wall effects. Consequently, in this investigation, the optical effect of glass is first studied. Then, with some minor modifications in the experimental setup and image processing technique, we accurately determined the glass effect. Then, it has been removed from the temperature and concentration measurement in post-


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processing of the MZI experiment. Using the proposed techniques yields an accurate, transient temperature measurement at any point in the cross section of the cell. To the best of our knowledge, this accurate measurement cannot be obtained using other techniques such as thermocouple sensors [1]. 2. MZI TO STUDY HEAT AND MASS TRANSFER PHENOMENON Speed of light varies in different media, depending on the material, concentration, and temperature. As a result, temperature and concentration can be measured using the change of refractive index using the contrast factors. There are two contrast factors with respect to change of temperature and concentration. The change of the refractive index can be measured using the Mach–Zehnder interferometry along the laser path. Contrast factors can be assumed as constant parameters with a slight change of other physical parameters. For example, the temperature contrast factor of a mixture represents the ratio of the change of refractive index caused by the change of temperature at a specific mean temperature. This coefficient at a specific concentration and small range of temperature variation can be used to extract the temperature variation from the change of refractive index [20]. Thus, MZI can be employed to visualize the temperature profile in any transparent media. A. Mach–Zehnder Interferometer Setup

A sketch of the Mach–Zehnder interferometry setup equipped with one laser source is shown in Fig. 1. There are two different paths for the laser beams: one goes through the experimental sample, and the other bypasses the cell through the void area and is used as a reference beam [21]. After passing the mirrors, the two beams interfered with each other at a second beam splitter and the end, interference fringes were captured by a charge coupled device (CCD) camera [4,19]. For the case of heat transfer study in the liquid, the cell, which contains the liquid, is located between the objective beam and second beam splitter close to the CCD camera. As shown, the temperature gradient can be applied along the Z direction, and temperature at points P 1 and P 2 can be read using some thermocouples,

Fig. 1. Sketch of Mach–Zehnder interferometer with single light source along with the cell heated from top.

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Research Article (FFT) image analysis along with windowed Fourier filtrations (WFF) have been used because of the strength and accuracy of the combination of the FFT and WFF for the investigation recently demonstrated by the heat and mass transfer experiment [1,2,17]. After extraction of the phase map for any image, the following formula presents the phase difference between the ith image (or any other image representing the initial condition) and the jth (or current image) [5,26]: Δϕx; y ϕi x; y − ϕj x; y:

(1)

Thus, the required phase difference, Δϕ or phase distribution can be obtained by the difference between the phase of the ith image and the reference image [27]. 3. CHANGE OF INDEX OF REFRACTIVE ALONG LASER PATH

Fig. 2. Sketch of a general quartz cell.

which are located inside the copper blocks on the top and bottom of the cell, while the change of refractive index integrated along the lines perpendicular to transparent purple plane can be measured using MZI. B. Cell Design

Because of the specific optical properties of the quartz material, the liquid container is made of quartz glass [22]. A general sketch of the quartz cell is demonstrated in Fig. 2. The liquid sample fills the central region of the cell and then the cell is sealed using O-rings at the walls. As mentioned, two copper blocks (high heat conductive material) are placed on the top and bottom of the cell. These blocks are in contact with the sample, and Peltier elements are positioned inside the blocks for heating and cooling the cell. It is obvious that, to measure the change of refraction for the sample inside the liquid region, the light source has to pass through the walls parallel with the z–x plane and along the y direction (see Fig. 2). This causes the change of refractive index due to change of the temperature at the walls; this effect is explained and determined in detail in Section 4.

In a general description, the accumulative phase change along the laser path, which is measured by interferometer, is caused by different sources such as air, glass walls, optical instruments, and liquid, as follows: ΔϕMZI Δϕliquid Δϕglasswalls Δϕair Δϕoptics :

(2)

By considering any image/phase map before applying temperature gradient as a reference image and subtracting it from the rest of images, which are taken in the presence of the temperature difference, the contribution of the air and the optics will be removed from the picture. This happens because any change of the temperature causes the change of refractive index inside the cell (liquid) and glass walls. However, the effects of air and optics between the reference image and other images remain constant and would be cancelled out by subtraction from the reference image; consequently, this can be expressed as follows because there are two glass walls: Δϕ ΔϕMZI − ΔϕMZI;ref Δϕliquid 2Δϕglasswall :

(3)

In the above equation, the contribution of the glass wall should be determined to find the exact contribution of the liquid in the change of phase. Note, the phase distribution yields the measurement of the refractive index according to the following equation [15,27]: λ Δnx; y nx; y − nref x; y Δϕx; y; (4) 2πL where L is the optical path length, defined as the distance in which the laser passes through the object or cell.

C. Experimental Sequences

This experiment has three straightforward steps: first, stabilizing the initial the temperature (and also concentration); then, imposing the second condition and proving enough time until reaching the steady condition; the last step is returning to the initial condition. During all of these steps, the interferometry fringe images are recorded by the CCD camera. D. Image Processing Technique

The application of Fourier fringe analysis or any other phaseextraction methods such as phase shifting can be used to obtain the phase distribution from the MZI fringe images [23–25]. Whereas in this study, the application of the fast Fourier

4. DETERMINATION OF THE GLASS WALL EFFECT As claimed in the first section, the effect of wall glass in the interferometry experiment to analyze the heat and mass transfer in the liquids is either neglected or estimated based on the rough approximation of the temperature refractive index of the cell material. In other words, since the optical properties of different glasses are not measured for all different wavelengths, the analysis of the glass effects in MZI is inaccurate. The relation that used to measure temperature difference without considering the impact of glass in previous studies is

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Δn ΔT MZI :

(5)

∂n ∂T liquid

However, here, two different techniques are introduced to accurately determine the effect of wall glass during the experiment. The first method suggests the integration of an additional light source, and the second method extract this effect by processing the optical phase change in the lateral walls. Below, two different experimental approaches are introduced that yield accurate measurement of the contribution of the wall glass in the MZI. A. Using an Additional Light Source with MZI

A general sketch of the Mach–Zehnder interferometer with two light sources is illustrated in Fig. 3. The apparatus consists of five parts: (1) laser sources and beam splitter; (2) reference lens and void area for the first path of the laser; (3) objective lens; (4) object or cell; and (5) CCD camera to capture interferogram. Based on the fringe pattern obtained by any of the lasers, a specific phase distribution can be obtained, and Eq. (3) can be rewritten as follows for each one of the light sources: Δϕi

2πW liquid 2πW cell − W liquid Δni;liquid Δni;glasswall ; λi λi (6)

where i represents the index for the ith laser, and Δn of the liquid and glass wall, which results due to the temperature difference, can be expressed as a function of temperature contrast factors of the glass and liquid as ∂n ΔT ; (7) Δni;liquid ∂T i;liquid Δni;glasswall

∂n ∂T

i;glasswall

ΔT :

Thus, the final form of Eq. (5) for the laser sources is 2πΔT ∂n W liquid Δϕ1 λ1 ∂T λ1 ;liquid ∂n ; W cell − W liquid ∂T λ1 ;glasswall

(8)

(9)

Δϕ2

2πΔT ∂n W liquid λ2 ∂T λ2 ;liquid ∂n W cell − W liquid : ∂T λ2 ;glasswall

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(10)

In Eqs. (9) and (10), there are three unknown parameters: temperature difference and temperature contrast factors of the glass at the wavelength of the first and second light sources. In order to solve this equation system, an additional equation is required. Next, the derivation of the third equation is explained based on the physical properties of the glass in which the minimum possible optical information of the glass is required. The refractive index of optical glasses changes with the change of the temperature; this change depends on the glass type and the wavelength. For instance, the refractive index of several glasses as a function of wavelength and temperature has been measured, and technical information is available [28], while it can be seen that some glasses have negative temperature coefficients in an optical system and some have positive. In addition, this coefficient slightly varies from one specific wavelength to another. This means that, for any specific glass at the specific operating wavelength, the temperature contrast factor must be measured; however, this technical information is not fully measured and can be found for few glasses. Alternatively, according to the measured data, there is a slight change of temperature contrast factor from one wavelength to another one when operating wavelengths are close (λ2 − λ1 < 0.5 μm). This condition is true for the specific range of the wavelength as 400 nm < λ < 1500 nm. This fact can be formulated as follows for available data in the literature [22,28]: ∂n ∂n ∂T λ ;glass − ∂T λ ;glass 1 2 −2.2 0.9 (11) λ 1 − λ2 This means that, when the wavelength of the laser increases, the temperature coefficient of refractive index decreases. Since the nominator in Eq. (11) is basically one order of magnitude greater than the denominator (for small change in the wavelength [λ2 − λ1 < 0.3 μm]), the temperature contrast factor can be assumed as a constant parameter; however, to obtain the most accurate result, the above relation has been used to complete the system of equations. Eventually, using the relations in Eqs. (9–11), all unknown parameters including ΔT can be measured. Finally, it should be emphasized that the effect of glass in the obtained temperature difference has been extracted from the measurement. B. Processing the Optical Data from Lateral Glass Walls

Fig. 3. Sketch of Mach–Zehnder interferometer with two sources.

In order to determine the effect of the transparent glass in the temperature measurement, the optical data obtained from the lateral walls during the experiment (monitoring the cell) is being analyzed for the second proposed technique in this study. Fig. 4 illustrates a general fringe image after the first thermal time and its phase map. The first thermal time means the time that a steady-state temperature profile in the domain is achieved. As illustrated, in the left-hand side of Fig. 4, in most cases when the fringe pattern is being recorded using MZI, part

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Fig. 4. Sample fringe image and its phase map in which few fringes are visible in the lateral glass walls.

of the lateral glass walls is also visible in the fringe map. This can be done using the advanced form of FFT, which is WFT. The change of fringe pattern in this region was neglected before due to two reasons. First, only a few fringes can be observed in the quartz region; second, processing such a narrow region requires an advance image processing technique. Processing this region is the key point to directly obtain the glass wall effect. Here, for the first time, we have processed the quartz wall region using WFT and filtration (WFF) [17,27,29]. In this method, instead of using the extra light source to have an extra equation, the optical data obtained during the experiment from the lateral walls are used. Thus, one light source is sufficient for this method to determine the effect of glass in the optical temperature measurement. As shown in the left-hand side of Fig. 4, enough fringes exist in the wall regions that can provide accurate phase information after image processing. Accordingly, few phase bands are visible in the glass region in the right-hand side of Fig. 4. Thus, the obtained information from this region is experimentally feasible enough to be used in the temperature measurement procedure, as follows, for the lateral glass walls:

∂n ∂T

λ1 ;glasswall

ΔT

λ1 Δϕlateral glasswalls ; 2πW cell

(12)

where Δϕ is the phase change in the lateral walls. Considering this question along with Eq. (9), both two unknowns [ΔT and ∂n λ1;glasswall ] can be calculated. Therefore, no optical informa∂T tion of the glass would be required for this measurement. C. Case Study: Space Experiment on Board the International Space Station

A series of experiments was conducted on board the International Space Station (ISS) to study the heat and mass transfer in some liquid mixtures under general supervision of NASA, ROSCOSMOS, and European Space Agency (ESA). The entire experiment is performed inside the microgravity lab located near the central axis of the station to have minimum perturbation of g-jitter vibration. The experiments were performed using the SODI apparatus (optical diagnostics instrument) equipped with a Mach–Zehnder interferometer with two laser sources at different wavelengths. The liquid mixture is located in a quartz Suprasil cell with specific dimensions.

Optical information of the liquid along with the dimensions of the cell is provided in Table 1. The experimental case was performed in three stages: half an hour at the constant temperature applied from two Peltier elements from the top and bottom of the cells (mean temperature of 298 K) and then several hours in the presence of a specific thermal gradient and, finally, returning the temperature of the walls to the initial mean temperature. According to the pervious study by Ahadi and co-workers [1,4], some fluctuations of the temperature variation between the walls were observed at the first stage. Value for the steady temperature gradient observed optically was about 10% less than the temperature, which is measured by the thermocouples [1,4]. The main reasons behind these nonconforming observations are addressed as follows: first, cropping the image and not considering the whole height of the cell and then the effect of the liquid container (glass wall effect). Here, we analyze the result of the space experiment in which the effect of walls is considered and the fringes for whole height of the cell are processed. Moreover, we have focused on the experimental time from the second stage when the temperature gradient is applied to system until the time that the steady state temperature variation was achieved. We monitored the refractive index variation inside the cell during this period, and, based on that, the temperature measurement has been conducted. Since there were some Table 1. Optical Properties of the Sample Liquid and Specifications of Cell Measured at Tmean 298K Symbol λ1 λ2 ∂n

∂T λ1;liquid

∂n ∂T λ2;liquid

Lcell W cell Lliquid W liquid H liquid

Quantity

Value and SI Unit

Wavelength of the first laser in the SODI apparatus Wavelength of the second laser in the SODI apparatus Temperature contrast factor of the liquid measured for the first laser Temperature contrast factor of the liquid measured for the second laser Length of cell Width of liquid region Length of liquid region Width of liquid region Height of liquid region

670 nm 935 nm −4.812 × 10−4 K −1 −4.763 × 10−4 K −1 3 cm 3 cm 1 cm 1 cm 5 mm

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Fig. 6. Cross section of the cell array used in the space experiment [1,30].

Fig. 5. Temporal ΔT measured by thermocouples.

thermocouples installed inside the apparatus along with the Peltier element to control the temperature difference between the hot and cold walls of the cell, the maximum temperature difference can be also measured using the thermocouples, which were located inside the copper blocks near the surface of the liquid. D. Results and Discussions 1. Temperature Measurement Using Thermocouples

As shown in Fig. 5, the temperature difference recorded by the thermocouples, which are located inside the copper blocks at the top and bottom of the liquid, is 10 0.2 K at the second stage of the experiment. 2. Optical Measurement, Neglecting the Effect of Glass

Unlike the temperature measured by the thermocouples, which shows ΔT 10 0.2 K, it can be seen in the right-hand side of Fig. 4 that there are 67 0.1 phase bands. Considering the wavelength of the laser (λ 670nm), it means the maximum refractive index difference between the top and bottom of the cell is Δn −4.489 × 10−3 based on Eq. (4). Substituting this value along with the temperature contrast factor in Eq. (5), one would end up with ΔT 9.33 K. This means about 7% variation between optical and thermocouple measurements. 3. Optical Measurement Using Two Light Sources

The maximum phase differences between the top and the bottom of the cell are −4.2096 × 102 and −2.9851 × 102 for lasers with a wavelength of λ1 670nm and λ2 935nm, respectively. Considering these number along with the temperature contrast factors of the mixture (see Table 1) and substituting them in Eqs. (9–11), the temperature difference will be measured as ΔT 9.53 K.

Composition between the temperature differences measured by the proposed techniques indicates an identical result with less than 0.1% variation. On the other hand, it can be concluded that the optical influence of the glass walls may affect the temperature measurement around 2%. Furthermore, it was observed that the temperature was underestimated using the optical technique in which the effect of glass was neglected. This is because the temperature contrast factor of the glass has a positive sign, while this optical parameter for the liquid has a negative sign. In general, when the container and the liquid mixture have a temperature contrast factor with an opposite sign, the optical measurement would underestimate the temperature variation; when they have temperature contrast factors with a similar sign, the optical measurement would overestimate the temperature variation. Finally, there is 5% variation between the temperature measured by the thermocouple and the proposed optical techniques. The main reason behind this variation can be explained as follows. The cross section of the cell array used in the space experiment is shown in Fig. 6. There are two holes for thermistors at the top and bottom of the cell to measure the temperature at these locations. However, it can be seen that these holes are not in direct contact with the liquid, and there were some gaps between the thermocouples and the liquid surface. Note, the thermocouples were located in the copper blocks, which has high thermal conductively; however, the temperature they sensed was not exactly the same as temperature sensed by liquid. In most of the other applications of thermocouples or thermistors, when they are used to measure the temperature of the liquid without disturbing the liquid domain, thermo sensors are not in direct contact with the liquid. This causes error in the temperature measure, while optical methods provide direct measurement of the temperature profile. Consequently, if the glass walls effect has been removed from the MZI method using the suggested technique, this optical technique can provide much more information from a domain with higher accuracy and precision.

4. Measurement Using Optical Data from the Lateral Walls

It can be seen in the right-hand side of Fig. 5 that there are 1.83 0.05 bands in the wall regions, which means Δϕ 11.49 or Δn 4.087 × 10−5 . Substituting this in Eq. (9) results in 9.52 K.

5. CONCLUSION The goal of this research (determination of the optical effect of glass walls in the heat and mass transfer experiment using MZI)

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was achieved either by proposing an extension to the processing of the results of the MZI experiment or by integrating an additional light source to the MZI setup. Particularly, when MZI is used to study the coupled heat and mass transfer, the effect of glass can be measured and removed from the processed results using any of the proposed techniques. In the first technique, in addition to analyzing the impact of heat and mass transfer on the liquid inside the cell, the effect of pure heat transfer on the lateral glass walls is separately but simultaneously analyzed. While, in the second method, the optical phase information from the secondary light source provides an additional relation that yields measurement of the glass wall impact. Comparison between the temperature measurements by any of these techniques with the temperature profiles obtained by thermocouple measurement indicates the accuracy of these techniques to determine the optical effect on the glass wall. Consequently, this effect can be deducted from other interferometry results and make possible the accurate optical measurement of the temperature variation along the glass wall and inside the liquid. The main advantages of using these temperature measurement methods in comparison with others such as thermocouple can be summarized as follows: (1) more accurate temperature measurement at any time during the experiment in which very small fluctuations of temperature can be detected (>0.005 K); (2) no contact with the medium, which avoids any disturbance in the fluid domain; (3) wide view of the temperature measurement at any location inside the cell (2D front view) and not only close to walls (use of thermocouple); (4) finally, using this method for MZI can result in a simpler measurement of heat and mass transfer in liquid by removing the thermocouple and replacing an online processing of the images. Canadian Space Agency (CSA); European Space Agency (ESA); Natural Sciences and Engineering Research Council of Canada (NSERC). A special thanks to the European Space Agency (ESA) and ROSCOSMOS for providing the authors with the raw data. REFERENCES 1. A. Ahadi and M. Z. Saghir, “An extensive heat transfer analysis using Mach Zehnder Interferometry during thermodiffusion experiment on board the International Space Station,” Appl. Therm. Eng. 62, 351–364 (2013). 2. A. Ahadi and M. Z. Saghir, “Experimental study of the impacts of forced vibration on thermodiffusion phenomenon in microgravity environment,” Appl. Therm. Eng. 60, 348–358 (2013). 3. R. J. Riobóo, M. Philipp, M. A. Ramos, and J. K. Krüger, “Concentration and temperature dependence of the refractive index of ethanol-water mixtures: influence of intermolecular interactions,” Eur. Phys. J. E. Soft Matt. 30, 19–26 (2009). 4. A. Ahadi, S. Van Varenbergh, and M. Z. Saghir, “Measurement of the Soret coefficients for a ternary hydrocarbon mixture in low gravity environment,” J. Chem. Phys. 138, 204201 (2013). 5. A. Ahadi, A. Kianian, and M. Z. Saghir, “Heat and mass transport phenomena under influence of vibration using a new aided image processing approach,” Int. J. Therm. Sci. 75, 233–248 (2014). 6. H. Svensson, “The second-order aberrations in the interferometric measurement of concentration gradients,” Opt. Acta Int. J. Opt. 1, 25–32 (1954).

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