JP2000258292A - Apparatus for measuring refractive index distribution and method for measuring refractive index distribution - Google Patents

Abstract

(57) [Problem] To provide an apparatus capable of easily superimposing measurement data and shape data of a test object in measurement of a refractive index distribution. SOLUTION: A light source 1, a test object holding device 10 having a test solution S having a refractive index substantially the same as the test object O, an interferometer for forming an interference fringe from a test wave transmitted through the test object, and the interference An imaging optical system 13 ′ for forming a fringe image, a moving device 37 for moving an object, an interference fringe detector 15, an arithmetic unit 39, and a second light source 25 incident on the imaging optical system And the reference plate 29
A configuration having: Prior to the measurement, the image of the reference plate 29 is formed on the interference fringe detector 15, the magnification of the image is obtained, and the measured data and the shape can be superimposed.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a technique for transmitting coherent light to a test object, forming interference fringes from the transmitted test wave, and measuring the phase distribution of the test object.

[0002]

2. Description of the Related Art In recent years, plastics have been increasingly used as materials for optical lenses used in optical devices such as laser printers and cameras. Compared to a glass polished lens, a plastic molded lens has advantages in that it is superior in cost reduction and manufacturability of an aspherical lens, and is inexpensive.

[0003] On the other hand, however, the refractive index distribution is unstable in production as compared with a glass lens, and non-uniformity may occur inside the lens. Non-uniformity inside the lens has a great effect on optical characteristics, leading to deterioration of image quality and blurring. Therefore, it is necessary to measure the refractive index distribution inside the lens three-dimensionally with high accuracy and evaluate the homogeneity of the optical lens.

As a method of measuring the refractive index of an optical lens, a method of measuring a refractive angle by a V-block method or the like using a precision differential refractometer or the like to obtain a refractive index, or an interference method such as a Twyman-Green interferometer or the like. There is a method of measuring the refractive index from the interference fringes using an interferometer, and the method of measuring optical homogeneity is based on the analysis of interference fringe images using an interferometer such as a Fizeau interferometer or a Mach-Zehnder interferometer. There is known a method of measuring a transmitted wavefront and obtaining optical homogeneity from a refractive index distribution.

However, in any of the above methods, the test object must be processed into a predetermined shape, and the optical element to be measured must be destroyed. Also, the refractive index distribution obtained from the transmitted wavefront becomes an average value integrated in the optical path traveling direction, and the three-dimensional spatial refractive index distribution is measured to specify the non-uniform refractive index part three-dimensionally. Can not.

In view of the above, the applicant of the present invention has proposed in Japanese Patent Application No. 6-203502 of the prior application that interference fringes are formed in a state where a test object is immersed in a test solution as shown in FIG. Has proposed a device for calculating the amount of transmitted wavefront from the above to measure the refractive index distribution.

[0007] The apparatus shown in FIG. 9 has a configuration using a Mach-Zehnder interferometer. The Mach-Zehnder interferometer includes a light source 1 for emitting laser light as coherent light, a beam expander 3, a light splitter 5 including a polarizing beam splitter,
Reflector 7 consisting of a mirror placed in the optical path of the reference wave
A reflection device 9 composed of a beam splitter that divides a test wave into two light beams; a polarization beam splitter serving as an optical superposition device 11; an imaging lens 13; and an interference fringe detector 15 composed of a CCD or the like. I have.

In FIG. 9, a test object O is located in a container-like test object support means 10 immersed in a test solution S having a refractive index substantially equal to that of the test object. Mouth 14
The optical flats 16 and 18 having good surface accuracy are attached to. The test object O has a rotation axis P perpendicular to the optical axis.
Object supporting means 1 which is installed on a turntable 20 having
Reference numeral 0 denotes a fixed state in which the test object 0 can rotate around the axis P. The rotation of the turntable 20 can be given a small rotation angle or a vertical movement, and a stepping motor or the like is used.

The laser beam emitted from the light source 1 is expanded in beam diameter by the beam expander 3, and is refracted at right angles by the beam splitter 5 to become a reference beam a. It is divided into a test wave b that passes through a phase object as O. The reference wave a and the test wave b are approximately 1:
It is set to 1.

The reflection device 7 is supported by an electric-displacement conversion element 19 such as a piezo element, and can change the optical path length of the reference wave a in the order of the wavelength or less in order to perform interference fringe analysis by the phase shift method. is there.

The reference wave a is reflected by the reflection device 7 and reaches the optical superimposer 11, while the other test wave b is transmitted through the test object O and a part b2 is reflected by the reflection device / light splitter 9, Although the light reaches the optical superimposer 11 and overlaps with the reference wave a, the electric-displacement conversion element 19 causes the optical path length between the reference wave a and the test wave b2 to be:
It is adjusted so as to have a phase difference of nπ / 2.

The reference wave “a” and the test wave “b” are superimposed, emitted from the optical superimposing device 11, enter the imaging lens 13 via the polarizer 17, and form an interference fringe on the imaging surface of the interference fringe detector 15. . As the interference fringe detector 15, a linear CCD, an area CCD, or an array sensor arranged in a direction orthogonal to the interference fringes is used.

The measurement result of the interference fringe detector 15 is expressed by a function of a transmitted wavefront W (x, y), where the length direction of the interference fringe detector 15 is x-axis, and the intensity generated by each element is W. You. One-dimensional CCD in which interference fringe detector 15 extends in the x-axis direction
In the case of (1), in one measurement, the transmitted wavefront can be measured for one measurement section obtained by cutting the test object in the xz plane.

By performing arithmetic processing such as Fourier transform and polar coordinate transform on the thus obtained transmitted wavefront W (x), a refractive index distribution N (x) can be obtained for the above-mentioned measured cross section. Then, the same measurement is performed for a plurality of locations on the y coordinate, and the refractive index distribution N (x, y) can be obtained.

According to the method and the apparatus for measuring the refractive index distribution according to the above-mentioned application, there is an advantage that high-precision measurement is possible without destroying the test object O at all and keeping the shape to be used. ing.

[0016]

However, in the above-described measurement of the refractive index distribution, it is necessary to superimpose the measured data of the refractive index distribution obtained from the interference fringe image and the shape data of the test object. is there. For this purpose, the magnification of the interference fringe image on the interference fringe detector must be known. However, conventionally, it is difficult to calculate the magnification, and it takes a long time to superimpose.

An object of the present invention is to solve such a problem, and an object of the present invention is to provide an apparatus for measuring a refractive index distribution which can easily obtain the magnification of interference fringes. Further, in the above-described related art, the length of the one-dimensional sensor of the interference fringe detector 15 is constant, while the size of the test object changes. As a result, the interference fringes may be too small or too large, resulting in poor measurement accuracy or inability to measure. SUMMARY OF THE INVENTION It is an object of the present invention to provide a refractive index distribution measuring apparatus capable of always forming an interference fringe image having substantially the same size without being influenced by the size of a test object.

Further, in the above-described measuring apparatus, if the light amount from the light source is too strong or too weak, accurate measurement cannot be performed. Therefore, it is an object of the present invention to provide a refractive index distribution measuring device capable of obtaining an appropriate amount of light.

Further, according to the above-mentioned measuring method, complicated arithmetic processing such as Fourier transform or polar coordinate transform is required. An object of the present invention is to provide a method capable of measuring a refractive index distribution by a relatively simple operation.

[0020]

In order to easily obtain the magnification of the interference fringe image, the apparatus for measuring the refractive index distribution according to the present invention employs a light source for emitting coherent light and a light beam emitted from the light source. A specimen holding device disposed above and having a sample liquid having substantially the same refractive index as the specimen and having mutually parallel entrances and exits;
An interferometer for forming an interference fringe on the measurement section, an imaging optical system for forming an interference fringe image formed by the interferometer, and a moving device for moving the test object in a direction crossing the one measurement section. An interference fringe detector provided at an imaging position of the interference fringe image;
Calculating means for calculating a refractive index distribution from the output of the interference fringe detector; a second light source incident on the imaging optical system;
And a reference plate provided between the light source and the optical system.

A light source driving device for controlling both the light source and the second light source, a configuration in which the two light sources are controlled so as not to be simultaneously lit, a configuration in which the optical system is a zoom lens, The transmission light amount changing means for changing the light amount of the light source may be provided, or the calculation means may be a calculation means for obtaining a polynomial approximation coefficient of the refractive index distribution by a polynomial approximation by the method of least squares.

As a method capable of measuring the refractive index distribution by a relatively simple calculation, a method of transmitting coherent light to a test object, forming an interference fringe image via an optical system, and Measurement of a refractive index distribution for obtaining a transmitted wavefront for one measurement section of the test object from the interference fringe image on the interference fringe detector provided and calculating a distribution of the refractive index for the one measurement cross section of the test object from the transmitted wavefront. In the method, a transmitted wavefront W (x ', y) is obtained by setting the measurement direction of the interference fringe detector to x', and an image of a reference pattern having a known length is formed on the interference fringe detector. A magnification M is obtained from the length of the image of the pattern by an arithmetic unit, and W (x,
y), and a refractive index distribution N (x, y) is further obtained.

From the transmitted wavefront W (x, y), the refractive index distribution N (x, y) is expressed as follows: N (x, y) = W (x, y) / d (x, y) (where d (X, y) is obtained from the thickness of the test object), and the arithmetic unit obtains a polynomial approximation coefficient of the refractive index distribution from the transmitted wavefront by a polynomial approximation by the least square method.

[0024]

Embodiments of the present invention will be described below in detail with reference to the drawings. FIG. 1 is a diagram showing an apparatus for measuring a refractive index distribution according to the present invention. Since most of the entire configuration of the apparatus shown in FIG. 1 is common to the conventional example, the description will be focused on the different configuration.

In the apparatus of the present invention, the transmitted light amount changing means 21 is provided between the light source 1 and the beam expander 3. The transmitted light amount changing means 21 is a disk-shaped ND filter, and is rotatably supported by a stepping motor 23. Then, the transmittance changes in the circumferential direction, and when rotated by the stepping motor 23, the transmission location of the ND filter changes, so that the intensity of the transmitted light can be changed. When the rotation angle of the stepping motor is determined, the transmittance is determined.

FIG. 2 is a diagram showing the output of the interference fringe detector. The vertical axis is the light intensity, and the horizontal axis is the pixel (x-axis). FIG.
Of the two parallel dotted lines in (a), the upper dotted line indicates the upper limit, and the lower line indicates the lower limit. If the output of the pixel is between the upper and lower limits, accurate measurement is possible.
If the value falls below the lower limit as shown in (b) or exceeds the upper limit as shown in FIG. 2 (c), accurate measurement cannot be performed.

In the apparatus of the present invention, the second light source 25, the collimator lens 27, and the reference plate 29 are arranged near the reflection device 9. The reference plate 29 is a rectangular opaque plate as shown in FIG. 3A, in which two slits 29a are formed in parallel at a known interval of L mm.

When the second light source 25 is turned on, it is collimated by the collimator lens 27 and illuminates the reference plate 29. Since the reference plate 29 is opaque and only the slit 29a is transparent, the light transmitted therethrough passes through the reflecting device 9 and is incident on the imaging lens 13, and the one-dimensional C of the interference fringe detector 15 is detected.
Image on CD.

FIG. 3B shows an output state of the interference fringe detector 15, in which the vertical axis represents light intensity and the horizontal axis represents pixels (x-axis). Since only pixels where light transmitted through the slit 29a forms an image receive a large amount of light, these distances L 'are measured.
The magnification M can be obtained from M = L / L ′.

FIG. 4 is a block diagram of the control part. The interference fringe detector 15 is connected to a CCD camera driving device 31, the stepping motor 23 is connected to a stepping motor driving device 33, and both the light source 1 and the second light source 25 are connected to a light source driving device 35. Light source driving device 35
Controls so that both the light source 1 and the second light source 25 are not turned on at the same time. Reference numeral 37 denotes an object moving device that moves the turntable 20 up and down in the y-axis direction. And these CCD
Camera driving device 31, stepping motor driving device 3
3. The light source driving device 35 and the object moving device 37 are connected to a personal computer 39, respectively, and are operated by instructions from a keyboard (not shown) by a program installed in the personal computer 39. In addition, each operation state and the interference fringe image formed on the interference fringe detector 15 are displayed on the display 41, so that the user can operate while visually confirming the operation.

In the apparatus according to the present invention, the imaging lens 13 is a varifocal lens. In particular, in the embodiment, a zoom lens is used so that an interference fringe image can be formed without changing the position of the interference fringe detector 15.

Next, the measuring method will be described. The measurement order proceeds in the order shown in the flowchart of FIG. That is, light quantity adjustment → acquisition of magnification → transmitted wavefront measurement →
Calculation of refractive index distribution → polynomial approximation. However,
The order of light amount adjustment and magnification acquisition can be interchanged.

First, the test object O is placed on the turntable 20, the light source 1 is turned on, and the interference fringe image is formed by the one-dimensional CC of the interference fringe detector 15.
An image is formed on D. Then, according to the flowchart of FIG. 6, the light amount is adjusted as follows.

First, the maximum value of the intensity is obtained from the pixel of the interference fringe detector 15 (S101). Then, it is determined whether the maximum value is below or above a preset upper limit (a dotted line in FIG. 2A) (S103).

If it is above the upper limit, it is determined whether or not the ND filter of the transmitted light amount changing means 21 has a margin for reducing the light amount (S105). If there is room to lower the transmission amount, an instruction is issued to the stepping motor driving device 33, and the transmitted light amount changing means 21 is rotated so that the transmitted light amount falls below the upper limit (S107). Next, returning to S101, the maximum value is obtained and compared again with the upper limit. However, since it should be lower than the upper limit, it is compared with the lower limit (S109). If it is above the lower limit, start the measurement.

If it is lower than the lower limit in S109, it is determined whether or not the ND filter of the transmitted light amount changing means 21 has room to increase the light amount (S111). If there is room to raise the transmission amount, an instruction is issued to the stepping motor driving device 33, and the transmitted light amount changing means 21 is rotated so that the transmitted light amount becomes higher than the lower limit (S113). If the transmitted light amount has already been exceeded and the transmitted light amount has been reduced, the rotation amount is set smaller than the previous rotation amount. As a result, the maximum value falls between the upper and lower limits.

If the maximum value is above the upper limit and there is no room to reduce the amount of transmitted light, or if the maximum value is below the lower limit and there is no room to increase the amount of transmitted light, a measurement impossible is displayed ( S115). Thus, the adjustment of the light amount is completed. The above operation is automatically performed by the personal computer 39.

Next, the imaging lens 13 'is operated so that the size of the interference fringe image on the interference fringe detector 15 becomes an appropriate size. This is done manually. In some cases, the maximum value changes due to the fluctuation of the interference fringe image. In such a case, the light amount adjustment is performed again.

Next, the light source 1 is transmitted through the light source driving device 35.
Is turned off, the second light source 25 is turned on, and a slit image of the reference plate 29 is formed on the interference fringe detector 15. And
Measure L ′ and calculate magnification M. This can be calculated by the personal computer 39 from the output of the one-dimensional CCD.

The interference fringe image is formed on the interference fringe detector 15 for one measurement section obtained by cutting the object O along the xz plane. Then, from the output of each pixel, W
(X ′, yi) is measured. This is the transmitted wavefront at y coordinate i. Since x ′ is a coordinate on a pixel, it is multiplied by a magnification M to obtain an x coordinate on the test object, and W (x, y
Obtain i).

The personal computer 39 issues an instruction to the object moving device 37, raises or lowers the object O, performs a plurality of transmission wavefront measurements on y0, y1, y2,. y0), W (x, y1), W
(X, y2) ... are obtained.

Assuming that the thickness of the test object is d (x, y) and the two-dimensional refractive index distribution is n (x, y), the following equation is obtained.

(Equation 1) Given by Here, d (x, y) is obtained from the design value of the shape data of the test object, the shape data of the test object obtained by shape measurement by another measuring device, or the like. The order of the polynomial approximation of the refractive index distribution is determined as needed. Here, the case of approximating the polynomial up to the fourth order will be described as an example.

The polynomial approximation of the refractive index distribution is defined as follows.

(Equation 2)

From equation (1), n (x, y) at each y value
i), and a refractive index distribution N ′ (x, yi) approximated by a polynomial is obtained from these.

(Equation 3)

FIG. 7 shows n (x, yi) and N '(x, yi)
Are illustrated in FIG. FIG. 7A shows y = y1,
(B) is an example of y = y2. A thin line having many fine bent portions in the figure is a refractive index distribution n (x, yi) obtained from the measurement data W (x, yi), and a refractive index distribution N ′ ( x, yi).

Each coefficient a '(i), b' in the above equation
(I), c ′ (i)... Can be obtained by polynomial approximation by the least square method. FIG. 8 shows a ′ (i) and b ′ (i) thus determined with a vertical axis representing a ′ or b ′.
This is displayed by taking y on the horizontal axis. As shown in these figures, a ′ (i) and b ′ (i) can also be represented as functions of y, and can be approximated by a polynomial as follows.

[0047]

(Equation 4)

The above coefficients a0, a1, a2,..., B
.. Can be obtained by the least squares method, and eventually a (y), b (y)... Can be obtained. By substituting these into equation (2), polynomial approximation can be obtained. The obtained refractive index distribution N (x, y) can be obtained.

The above calculation is performed by the personal computer 3
By installing the program on 9,
It is possible to do. This calculation method is simpler than the calculation method combining the Fourier transform and the polar coordinate transform, so that the measurement can be performed in a short time.

Although the above-described embodiment uses the Mach-Zehnder interferometer, other interferometers can also be used for measurement. In addition, the test wave is divided into two without using the reference wave, and the lateral shift is performed. Measurements can also be made with the shearing interferometer provided.

[0051]

As described above, the refractive index distribution measuring apparatus according to the present invention comprises a second light source incident on an imaging optical system and a reference provided between the second light source and the optical system. With the provision of the plate, the magnification of the interference fringes can be easily obtained, and the measurement data and the shape data of the test object can be easily superimposed.

When a light source driving device for controlling both the light source and the second light source is provided so that the two light sources are not turned on at the same time, a measurement error caused by turning on both light sources can be prevented. it can.

When the optical system is a zoom lens, the size of the interference fringe image can be freely changed, and the measurement becomes easy. If the transmitted light amount changing means is provided, the light amount of the light source can be changed to perform measurement with an appropriate light amount, and the measurement accuracy can be improved. If the measurement data is processed by the polynomial approximation, the arithmetic processing is simplified and the measurement time can be reduced. Further, if it can be represented by a coefficient by polynomial approximation, a complex refractive index distribution can be represented by several numbers, and input to an optical simulation or the like using the measured refractive index distribution can be simplified.

[Brief description of the drawings]

FIG. 1 is a diagram showing a configuration of a refractive index distribution measuring device of the present invention.

FIG. 2 is a diagram showing an output state of an interference fringe detector.

3A is a diagram of a reference plate, and FIG. 3B is a diagram illustrating an output state of an interference fringe detector when an image is formed on the reference plate.

FIG. 4 is a block diagram of a control part of the apparatus of FIG. 1;

FIG. 5 is a flowchart showing a measurement order of the apparatus of FIG. 1;

FIG. 6 is a flowchart for performing light amount adjustment.

FIG. 7 is a diagram showing a relationship between n (x, y) and N ′ (x, y).

FIG. 8 is a diagram illustrating how to obtain a (y) and b (y).

FIG. 9 is a diagram showing a configuration of a conventional refractive index distribution measuring device.

[Explanation of symbols]

 Reference Signs List 1 light source 10 subject holding device 13 'imaging optical system 15 interference fringe detector 21 transmitted light amount changing means 25 second light source 29 reference plate 35 light source driving device 37 moving device 39 calculating device

Claims (7)

[Claims] 1. A light source for emitting coherent light, a sample liquid having a refractive index substantially the same as that of a test object arranged on a light beam emitted from the light source, and an entrance and an exit parallel to each other. An object holding device, an interferometer for forming an interference fringe for one measurement section of the object from a test wave transmitted through the object, and an imaging optics for imaging an interference fringe image formed by the interferometer A system, a moving device for moving the test object in a direction crossing the one measurement section, an interference fringe detector provided at a position where an interference fringe image is formed, and a refractive index distribution based on an output of the interference fringe detector. , A second light source incident on the imaging optical system, and a reference plate provided between the second light source and the optical system. Measuring device. 2. The refractive index distribution according to claim 1, wherein a light source driving device for controlling both the light source and the second light source is provided, and the two light sources are controlled so as not to be turned on at the same time. measuring device. 3. An apparatus according to claim 1, wherein said optical system is a zoom lens. 4. The apparatus for measuring a refractive index distribution according to claim 1, further comprising a transmitted light amount changing means for changing the light amount of the light source. 5. The apparatus for measuring a refractive index according to claim 1, wherein said calculating means is a calculating means for obtaining a polynomial approximation coefficient of a refractive index distribution by a polynomial approximation by a least square method. 6. Transmitting the coherent light to the test object, forming an interference fringe image via an optical system, and detecting the interference fringe image from the interference fringe image on the interference fringe detector provided at the imaging position. In a method for measuring a refractive index distribution for obtaining a transmitted wavefront for a measurement section and calculating a refractive index distribution for the one measurement section of the test object from the transmitted wavefront, the transmitted wavefront is defined as x ′ in the measurement direction of the interference fringe detector. W
(X ′, y) is obtained, an image of a reference pattern having a known length is formed on the interference fringe detector, and a magnification M is obtained from a length of the image of the reference pattern by an arithmetic unit. A W (x, y) is calculated from the magnification M by x = Mx ′, and a refractive index distribution N (x, y) is further obtained. 7. From the transmitted wavefront W (x, y), the refractive index distribution N (x, y) is given by N (x, y) = W (x, y) / d (x, y) where: d (x, y) x, y) is determined by the thickness of the test object,
7. The method of measuring a refractive index distribution according to claim 6, wherein the arithmetic unit obtains a polynomial approximation coefficient of the refractive index distribution from the transmitted wavefront by a polynomial approximation by the least square method.