KR20110031766A - Measurement of refractive index of wafer-type media by utilizing interference of transmitted and reflected beams - Google Patents

Abstract

PURPOSE: A system and a method for measuring the refractive index of a plate-shaped sample using the interference of transmitted light and reflected light are provided to cost-efficiently and accurately measure the refractive index of plate-shaped media. CONSTITUTION: A system for measuring the refractive index of a plate-shaped sample using the interference of transmitted light and reflected light comprises a laser light source(11), a light detecting unit(14), and a calculation unit. The laser light source irradiates beams to a plate-shaped sample(13). The light detecting unit measures the intensity of transmitted light or reflected light from the laser light source. The calculation unit calculates the relative refractive index and thickness of the sample.

Description

System and method for measuring refractive index of flat media using interference between transmitted and reflected light {Measurement of refractive index of wafer-type media by utilizing interference of transmitted and reflected beams}

The present invention relates to a system and method for measuring refractive index of a plate-shaped medium using interference between transmitted light and reflected light. Particularly, the present invention provides a refractive index measurement system of an optical medium that can measure the refractive index, and further, the thickness of a flat sample by using the multi-reflection light and the transmitted light interference phenomenon of the flat sample itself that can be easily obtained from the surrounding area. It is about a method.

The refractive index of the optical medium is very important information for the prediction and interpretation of the results of all optical experiments. In particular, as various optical technologies have been developed since the invention of the laser, the characteristics of the optical medium have become essential information in the field of application thereof. Accurate refractive index (dispersion) is essential for calculating phase-matching conditions for efficient generation of optical harmonics in nonlinear optics, for predicting group speed and optical pulse dispersion in optical fiber communications, and for precise optical component design. to be.

To date, various methods of measuring the refractive index of an optical medium have been researched and developed, but in many cases, it is necessary to produce samples of low accuracy or a specific type of measured refractive index.

For example, in the method of measuring refractive index of plate glass of Korean Patent Publication No. 10-2009-7134, the refractive index of the plate glass is measured in a non-contact manner by using a laser light output device and an imager disposed on the upper portion of the plate glass. Should be measured by a separate equipment, and the thickness of the plate glass should be homogeneous, so the size of the laser beam used is very precise because the precision of the refractive index is determined.

In addition, in the method and apparatus for measuring the thickness of a transparent material, Korean Patent No. 10-0721783 discloses a focus of a light beam having a modulated light frequency on a transparent material, and includes two light beams reflected from each side of the transparent material. Since the light beam is received and the interference is generated between the two light beams, the frequency per modulation period of the interference signal is determined, the path difference between the two beams and the thickness of the transparent material are inferred, and also the phase shift of the interference signal is determined. Invented by the wave optical method for measuring the thickness of a transparent material having a refractive index (n), or on the premise of thickness measurement, the refractive index of the transparent material is separately measured, and is suitable for measuring the thickness of a material larger than 0.2 mm. There is a problem that it is difficult to measure.

The present invention for solving the conventional problems as described above is a wave optical method using the interference phenomenon of the multi-reflection light and the transmitted or reflected light of the flat sample surface without being greatly influenced by the state of the sample simple and low cost The aim is to measure accurate refractive indices and to enable high precision thickness measurements with a single instrument.

According to the present invention for achieving the above object, the refractive index measurement system of the plate-shaped medium using the interference of the transmitted light and the reflected light, the laser light source for irradiating a beam to the flat sample; Light detecting means for measuring the intensity of transmitted or reflected light of an interference fringe due to multiple reflections of a laser beam from the laser light source passing through the flat sample as a function of incident angle; And a phase difference between two neighboring beams (Equation 1) for obtaining the intensity I _T (θ) of the transmitted or reflected light due to the superposition of electric fields when the incident angle of the laser beam is θ for the plate-shaped sample. Equation (2) to obtain the incidence angles of the maximum or minimum points of the theoretical transmitted or reflected light intensity of the transmitted light intensity, and compare them with the incidence angles of the maximum or minimum points measured by the light detection means, And calculating means for obtaining a relative refractive index n _r and a thickness d which give the smallest error by 3.

Where Equation 1 is

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Equation 2 is

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Equation 3 is

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t = transmission coefficient, t '= transmission coefficient when light is incident from the inside of the sample, r' = reflection coefficient when light is incident from the inside of the sample, na = refractive index of air.

In another aspect, the present invention is characterized in that, when the flat sample is an anisotropic medium, a polarizer for distributing only linearly polarized light parallel to one crystal axis of the laser beam between the laser light source and the flat sample. .

In addition, the present invention is to measure the intensity of the transmitted or reflected light by sampling the interference fringe while adjusting the angle of incidence (θ) of the laser beam by rotating the rotating stage for supporting the flat sample by a stepping motor (stepping motor) Characterized in that.

In addition, the present invention is characterized in that a silicon photo diode or a solar cell is used as the light detection means when the beam wavelength of the laser light source is 400 nm to 1,100 nm region.

In addition, the present invention is characterized in that a germanium diode is used as the light detection means when the beam wavelength of the laser light source is in the 1,100 nm to 1,700 nm region.

In another aspect, the present invention is characterized in that the strip type solar cell is used as the light detection means when measuring the reflected light reflected by the flat sample to obtain the intensity of the reflected light.

In addition, the method for measuring the refractive index of the plate-type medium using the interference of the transmitted light and the reflected light according to the present invention, the first step of irradiating the plate-type sample with a beam from the laser light source; A second step of measuring the intensity of transmitted or reflected light of the interference fringe due to multiple reflections while passing through the flat sample; And a phase difference between two neighboring beams (Equation 1) for obtaining the intensity I _T (θ) of the transmitted or reflected light due to the superposition of electric fields when the incident angle of the laser beam is θ for the plate-shaped sample. Equation 2 is obtained from Equation 2 to obtain the incidence angles of the maximum or minimum points of the theoretical transmitted or reflected light intensity of the transmitted light intensity, and compares them with the incident angles of the maximum or minimum points measured in the second step, The third step of obtaining the relative refractive index (n _r ) and the thickness (d) giving the smallest error by; characterized in that it comprises a.

Where Equation 1 is

이고,

ego,

Equation 2 is

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,

Equation 3 is

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to be.

In addition, the present invention is to measure the intensity of the transmitted or reflected light by sampling the interference fringe while adjusting the angle of incidence (θ) of the laser beam by rotating the rotating stage for supporting the flat sample by a stepping motor (stepping motor) Characterized in that.

Therefore, according to the present invention, the present invention has the effect of determining the refractive index of the optical medium with an accuracy of about 10 ^-5 by improving the analysis method of the refractive index results and supplementing the measurement system.

In addition, the present invention is simpler than the conventional methods by measuring the refractive index of the wafer-type optical medium by using an interferometer using multi-interference, which is useful for establishing a dispersion formula of a new optical medium because it is simpler, more stable to environmental changes, and higher in accuracy. Do.

1 is a system configuration according to the present invention for measuring the transmitted light interference fringes of the transmitted light multi-reflection to measure the refractive index of the flat sample.

First, the laser light source 11 irradiates a laser beam for measuring the refractive index of the flat sample 13, and a DFB laser, a He-Ne laser, or the like is used. The light detecting means 14 is disposed on the opposite side of the flat sample 13 at a predetermined distance in front of the laser light source 11.

Here, the light detecting means 14 measures the intensity of the transmission or reflected light of the interference fringe due to the multiple reflection of the laser beam passing through the plate-shaped sample 13, and is made of silicon photo diode, solar cell, germanium diode, strip type. Solar cells and the like can be used.

In detail, a silicon photo diode or a solar cell may have a strip when the laser light source 11 has a beam wavelength of 400 nm to 1,100 nm, and a germanium diode may have a strip when the laser light source 11 has a beam wavelength of 1,100 nm to 1,700 nm. The solar cell of the type can be used when measuring the reflected light reflected by the flat sample 13 to obtain the intensity of the reflected light.

In addition, when the flat sample 13 is an anisotropic medium, a polarizer for passing only linearly polarized light parallel to one crystal axis of the laser beam is disposed between the laser light source 11 and the flat sample 13.

The rotating stage 15 supporting the plate-shaped specimen 13 is rotated by a predetermined angle using a stepping motor (not shown) to adjust the incident angle θ of the laser beam while sampling the interference fringe to transmit or Allows you to measure the intensity of the reflected light.

 Although not shown in the drawing, a calculation means such as a PC or a notebook is connected to the light detecting means 14 to connect the calculation means of the flat sample 13 by using the intensity of the transmitted or reflected light measured by the light detecting means 14. The refractive index, and further, the thickness of the flat sample 13 can be calculated.

Hereinafter, a process of calculating the refractive index by a computing means such as a PC or a laptop will be described.

First, the laser beam (plane wave) emitted from the laser light source 11 undergoes multiple reflections as shown in FIG. 2 while passing through the planar sample 13, and when the external incidence angle is θ , the calculation means is expressed by Equation 2 below. The phase difference between two neighboring beams can be obtained.

Where ? Is the wavelength in vacuum of the beam (light), d is the thickness of the flat sample 13, n _a is the refractive index of the ambient air and n _r is the relative refractive index of the flat sample 13 with respect to air. The electric fields 1, 2, 3, ... of the light beams passing through the flat sample 13 overlap each other, as shown in Fig. 2, and are caused by the phase difference Φ that varies according to the angle of incidence. Show the pattern.

The intensity of transmitted light due to the superposition of these electric fields is obtained by Equation 1 below.

Where r and t are reflection coefficients and transmission coefficients, respectively, and prime means transmission or reflection inside a medium. That is, t '= transmission coefficient when light is incident from the inside of the sample to the outside, and r' = reflection coefficient when light is incident from the inside of the sample to the outside. They are given by the Fresnel equation once the relative refractive index, angle of incidence, and polarization direction are determined.

Figure 3 shows the transmission (top) and reflection (bottom) interference fringes ( n = 1.5000, d = 1.0000 mm, λ = 633.00 nm) and is a typical graph of the intensity of transmitted and reflected light with incident angle. In both cases, the interference fringes complement each other, and in the case where the relative refractive index is small, the transmitted light interference fringes may be difficult to obtain experimentally due to the low contrast ratio. Although the shadow ratio is much better reflected light, it is difficult to track the reflected light according to the rotation angle.

4A and 4B are graphs comparing the spacing and phase difference between the Michelson interferometer and the multi-reflective interference fringe. As shown in the figure, when the refractive index is measured by a Michelson interferometer, the change in phase difference increases as the rotation angle of the flat sample increases, so that the spacing of the interference fringes is narrowed, while the interference fringes due to the multi-reflection interference have a specific angle abnormality. As a result, the rate of change of the phase difference decreases, and the interval between the interference fringes becomes wider. In the Michelson interferometer, the larger the refractive index of the flat sample and the thicker, the narrower the pattern spacing, thereby limiting the selection of the flat sample, but in the case of the multi-reflection interference, the selection of the flat sample is relatively wide.

Hereinafter, more specific experimental examples will be described.

The use of optical wafers with already well known refractive indices confirms the effectiveness of the method according to the invention. In the wide wavelength region, an optical medium in which the Selmeier equation is well known may be fused silica glass. In order to determine the refractive index with an accuracy of about 10 ^-5 , most experimental variables should be defined with more than this accuracy. As can be seen from Equation 1, the wavelength, the thickness of the flat sample, the refractive index of the air, etc. should be accurately known, and the intensity of the transmitted or reflected light should be measured while changing the incident angle in as small steps as possible.

First, a DFB laser whose line width is very narrow and whose frequency is stabilized is used as the laser light source to be used. In the experimental example of the present invention, a DFB laser having a center wavelength of about 1550 nm is first used, and then measured using a He-Ne laser (wavelength 633 nm). The wavelength of the DFB laser can be measured with an optical spectrum analyzer or wavelength meter with an accuracy of 10 pm.

However, the thickness of a flat sample is very difficult to measure with an accuracy of about 10 ^-5 . Too thick plate-shaped samples have a narrow interference fringe, so that the method according to the present invention cannot be applied, and a thickness of about 1 mm is generally used. Nevertheless, it is not easy to measure thicknesses down to 0.01 μm with an accuracy of around 10 ^-5 .

At present, the accuracy of the thickness measured and guaranteed by the Korea Research Institute of Standards for typical flat samples is 0.1 μm.

Furthermore, when the plate-shaped sample is mounted on the rotating stage, the beam (light) passes through a distance greater than the actual thickness if the axis of rotation and the optical path are not exactly vertical. However, as explained below, the thickness can be measured to some extent to determine the exact value with the interference fringe fitting along with the refractive index.

Therefore, it is important to know the thickness of the flat sample accurately and to make the flat sample perpendicular to the optical path, but in practice, it is necessary to accurately determine the thickness by fitting in consideration of the slight inclination. In the present invention or the experimental example of the present invention, the inclined angle of the flat sample can be maintained within 0.1 degrees, and this means a thickness error within 10 ^-6 , and thus does not actually affect the measurement (experimental) result analysis.

Using a stepping motor as a power source for rotating a wafer, that is, a flat sample mounted on a rotating stage, it is possible to accurately sample an interference fringe at a step of incident angle up to 0.004 degrees. However, since the absolute value of the angle is important, the exact size of one step must be determined by rotating the flat sample, ie, wafer, by 180 degrees and counting the number of steps.

The refractive index of air is about 1.0003 under standard conditions. When the refractive index is measured in the air, if the air refractive index is ignored, the absolute refractive index value of the flat sample is 10 ^-4 or more. Since the refractive index of air is a function of air pressure, humidity, etc., measure it in a laboratory atmosphere, and calculate the air refractive index with an accuracy of 10 ^-5 and correct it.

As in the description of FIG. 1, a Si-photodiode is used in the visible light to a wavelength of 1100 nm, and a Ge-photodiode is used in the light detector. In addition, when measuring the refractive index of the anisotropic medium, the polarizer is placed in front of the flat sample, and the linear polarization parallel to one crystal axis is selected and tested.

The analysis method for the above experimental results is as follows.

As a result of the above experiment, the interference fringes of the multi-reflected light show a vibration shape according to the incident angle (rotation angle of the flat sample). When the refractive index of the flat sample is small and the surface reflection is not large, the intensity distribution of the interference light has a sinusoidal shape, and the interval between the patterns tends to narrow as the incident angle increases. However, the higher the refractive index of the medium, the greater the surface reflection, and the peak point is pointed out when the transmitted light is measured, indicating a typical Fabry-Perot interferometer.

Theoretically, the interference fringe is exactly symmetrical to the left and right with respect to zero degrees, so this fact is used to determine zero degrees from the measured I (θ) data. An interference pattern I (θ) measured by transmitting a DFB laser beam through fused silica glass is shown in FIG. 5.

This phase change and the period of continuous change of data does not have a proper model for fitting, and requires a lot of time if manual fitting. Thus, in the present invention, this data is converted into a form that is easy to fit.

That is, the number of interference fringes and the position of local maxima or minima ( θ _i ) are obtained from the experimental data, and once the approximate refractive index and thickness are determined only by the number of local maxima or minima, Fine-tune the refractive index and thickness values to select the refractive index and thickness where the positions of the maximum points most closely match the experimental values. In this way, the refractive index and the thickness are simultaneously determined in the present invention and the experimental example of the present invention.

Detailed interpretation is described below, where local maximum points are selected and analyzed.

First, look at the process of determining the position (θ _i) of the maximum point, a correction to the interference pattern data, such as five degrees 0 obtained in the experiment, and then matched matrix (array) the angle sequence (i) and for each maximum point θ _exp Find _i . In practice, the flat sample is rotated one step at a constant small angle (0.004 degrees) while measuring the intensity of the transmitted light.

The maximal point of the interference fringe is usually located between two sampling angles. An error occurs when the position of the maximal point is selected by selecting the closer angle between the two sampling angles. To solve this problem, we fit a quadratic function near each maximal point of each fringe to determine the vertex as the location of the maximal point.

Fig. 6A can complement the limited precision of the rotary stage used in the present invention in this way with a mathematical method. As shown in FIG. 6B, a matrix in which the order of the interference fringes and the positions of the fringes is determined as a graph is shown in FIG. 6B, and a graph having such a trend can be easily fitted.

Next, looking at the process of determining the approximate refractive index and thickness by the number of maximum points, the approximate refractive index and thickness can be obtained from the local maxima or the location ( θ _i ) matrix obtained as described above. Equation 2, which calculates the phase difference, is inserted into the cosine of Equation 1 of the intensity distribution according to the angle when the transmitted light is measured. Therefore, the maximum point of the interference fringe appears when Equation 2 = 2 π m ( m is an integer).

Therefore, the number of maximum points ( m ₀ - m _max ) can be obtained by comparing the m value m ₀ obtained when θ is 0 with the m value m _max obtained by substituting θ of the position of the last maximum point. Comparing this with the size of the matrix obtained from the data gives an approximate refractive index value n _temp .

However, in this case, since the thickness value needs to be known to some extent, the thickness ( d _temp ) of the flat sample is measured to 1 μm using a conventional micrometer. The refractive index values thus determined typically have an error of about 3 × 10 ⁻³ .

Next, in the process of precisely determining the refractive index and the thickness value by fitting, it is necessary to obtain a more accurate refractive index value by comparing with the surrounding values from the rough refractive index and thickness values obtained as described above.

To this end, the calculating means systematically calculates an error map for the refractive index and the thickness within a predetermined range from the value predicted above.

First, the position matrix θ _{i, temp} of the maximum points is obtained by using Equation 1 for the variable set ( n, d ) _temp . To find the true value ( n, d ) _real , obtain θ _{theo, i} for ( n, d ) values slightly out of the range of refractive index and thickness centered on ( n, d ) _temp . Find the chi-square sum of the maximum position deviations, as shown in

Fig. 7 shows its inverse 1 / ΣChi-square as a function of (n, d), and Fig. 7a is a 1 / ΣChi-square error map for (n, d), with the two axes on the bottom representing the n and d axes, respectively. FIG. 7B shows the contour plot in FIG. 7A with the arrow pointing to the true value (n, d) _real .

Theoretically, the (n, d) value is the true value (n, d) becomes larger so that the peaks of the near match the _real, is that the height infinity when it clicks. In practice, however, due to various experimental errors, not only the peaks around the true value but also some peaks around them are observed to have similar heights, and therefore, in FIG. 7A, a large number of ( n, d ) variable groups can be obtained as a fitting result.

Therefore, in the present invention and the experimental example of the present invention, the thickness of the flat sample was measured more accurately than 1 μm in order to remove such uncertainty. In the contour plot of FIG. 7B, the distance between two neighboring peaks is about 0.4 μm, so in this experimental example, it is sufficient to measure the thickness of the flat sample with an accuracy of 0.3 μm. In this way, when the uncertainty of several peaks is eliminated, the result of the fitting is performed only within one peak, and the accuracy exceeds the precision of the thickness measurement. The fitting method used the Simplex method, and the refractive index was determined to be 1.444432 ± 0.000007 and the thickness was 1085.48 ± 0.01 μm on a DFB laser (wavelength 1529.2 nm) for the molten silica glass flat plate sample.

As shown in Equation 1, the longer the wavelength, the thinner the plate-shaped sample, and the smaller the refractive index, the further the distance between the peaks on the error map, so that the thickness accuracy may be lower.

However, at short wavelengths, there is a difficulty in measuring thickness more accurately than this. However, this also can be overcome by the improvement of the system and method according to the present invention. That is, in the experiment, the light path of the long wavelength and the light path of the short wavelength are matched with each other, and then the thickness of the light passing point is accurately determined using the measurement result of the long wavelength light. When fitting the results of short wavelength light, the thickness is fixed to the value obtained earlier and only the true value of the refractive index is found. By this method, the refractive index of the fused silica glass plate sample in the He-Ne laser (wavelength 632.99 nm) was determined to be 1.457187 ± 0.000011 and the thickness was 1085.48 ± 0.01 μm (the same as in the DFB laser experiment).

1 is a system configuration according to the present invention for measuring the transmitted light interference fringes of the transmitted light multi-reflection to measure the refractive index of the flat sample.

2 is a diagram showing a multiple reflection optical path in a flat sample.

Figure 3 shows the transmission (top) and reflection (bottom) interference fringes ( n = 1.5000, d = 1.0000 mm, λ = 633.00 nm) and is a typical graph of the intensity of transmitted and reflected light with incident angle.

4A and 4B are graphs comparing the spacing and phase difference between the Michelson interferometer and the multi-reflective interference fringe.

5 is a graph showing the distribution of the intensity of transmitted light according to the incident angle (synthetic quartz, wavelength 1529.174 nm, n _a = 1.00027).

Fig. 6A shows a method of determining the position of one maximum point in the interference fringe, and Fig. 6B is a graph showing the sequence and position of the resulting maximum point.

7A is a 1 / ΣChi-square error map for (n, d), with the two axes on the bottom representing the n and d axes, respectively.

FIG. 7B is a contour plot in FIG. 7A with arrows pointing to true values (n, d) _real .

-Explanation of symbols for the main parts of the drawings

11 laser light source 12 polarizer

13: flat sample 14: light detecting means

15: rotating stage

Claims (8)

A laser light source for irradiating a beam onto the flat sample; Light detecting means for measuring the intensity of transmitted or reflected light of an interference fringe due to multiple reflections of a laser beam from the laser light source passing through the flat sample as a function of incident angle; And Equation 1 for obtaining the intensity (I _T (θ)) of transmitted or reflected light due to superposition of electric fields when the incident angle of the laser beam is θ for the plate-shaped sample, and the phase difference Φ (θ) between two neighboring beams Equation 2 to obtain the incidence angles of the maximum or minimum points of the theoretical transmitted or reflected light intensity of the transmitted light intensity, and compare them with the incident angles of the maximum or minimum points measured by the light detection means, Calculating means for obtaining a relative refractive index n _r and a thickness d which give the smallest error; Refractive index measurement system of the plate-type medium using the interference of the transmitted light and the reflected light, characterized in that it comprises a. Where Equation 1 is

ego, Equation 2 is

, Equation 3 is

to be. The method of claim 1, When the flat sample is an anisotropic medium, a polarizer for passing only linearly polarized light parallel to one crystal axis of the laser beam is disposed between the laser light source and the flat sample. Refractive Index Measurement System of Flat Media Using Interference. The method of claim 1, Rotating the stage supporting the plate-shaped sample by a predetermined angle by using a stepping motor (stepping motor) by adjusting the incident angle (θ) of the laser beam while sampling the interference fringe to measure the intensity of the transmitted or reflected light Refractive index measurement system of the plate-type medium using the interference of the transmitted light and reflected light. The method of claim 1, When the beam wavelength of the laser light source is 400 nm to 1,100 nm region, a silicon photo diode or a solar cell is used as the light detection means, the refractive index measurement system of the flat plate medium using the interference of the transmitted light and the reflected light. The method of claim 1, And a germanium diode as the light detection means when the beam wavelength of the laser light source is in the range of 1,100 nm to 1,700 nm. The refractive index measurement system of a flat plate medium using interference between transmitted light and reflected light. The method of claim 1, In the case of obtaining the intensity of the reflected light by measuring the reflected light reflected by the flat sample, a strip type solar cell is used as the light detection means, the refractive index measurement system of the flat plate medium using the interference of the transmitted light and the reflected light . Irradiating a beam from the laser light source onto the flat sample; A second step of measuring the intensity of transmitted or reflected light of the interference fringe due to multiple reflections while passing through the flat sample; And Equation 1 for obtaining the intensity (I _T (θ)) of transmitted or reflected light due to superposition of electric fields when the incident angle of the laser beam is θ for the plate-shaped sample, and the phase difference Φ (θ) between two neighboring beams Equation 2 to obtain the incidence angles of the maximum or minimum points of the theoretical transmitted or reflected light intensity of the transmitted light intensity, and compare them with the incidence angles of the maximum or minimum points measured in the second step, Obtaining a relative refractive index (n _r ) and a thickness (d) giving the smallest error by using the third step; Refractive index measurement method of the plate-type medium using the interference of the transmitted light and the reflected light, characterized in that it comprises a. Where Equation 1 is

ego, Equation 2 is

, Equation 3 is

to be. The method of claim 7, wherein Rotating the stage supporting the plate-shaped sample by a predetermined angle by using a stepping motor (stepping motor) by adjusting the incident angle (θ) of the laser beam while sampling the interference fringe to measure the intensity of the transmitted or reflected light Method for measuring the refractive index of the plate-type medium using the interference of the transmitted light and the reflected light.

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