JP2678464B2 - Refractive index measurement method - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a refractive index measuring method, and is particularly suitable for measuring a refractive index and a refractive index distribution of a plastic lens whose shape and refractive index are unknown. It also relates to a refractive index measuring method.

[Prior Art] Plastic lenses reduce the weight and cost of lenses.
Or, due to the need for aspherical lenses, etc., they have been widely used in recent years.

However, from the viewpoint of stability of the physical properties of the plastic lens, there is a drawback in that the refractive index and its distribution are unstable and the fluctuation thereof is large in manufacturing, as compared with the glass lens. Therefore, it is necessary to measure the refractive index and its distribution of each plastic lens one by one after molding. In this case, the lens cannot be destroyed, so the measurement is not easy. Especially if it is an aspherical lens.

Conventionally, there have been the following methods for measuring the refractive index of such a plastic lens.

The device used is a Mach-Zehnder interferometer as a whole, using one light beam as the reference light of the plane wave, and matching the test lens in the other light beam with a refractive index almost equal to that of the test lens. Set by immersing in liquid. Further, as a reference for the refractive index, a glass sample having a refractive index close to the lens to be inspected and having a known refractive index is simultaneously immersed in the liquid and set. In observing interference fringes generated by placing such an immersion device in one beam of a Mach-Zehnder interferometer, N
The difference in the thickness of the sample was measured while the interference fringes of the book were observed, and the refractive index of the lens under test was determined from the measured value.

[Problems to be Solved by the Invention] However, the refractive index of the matching liquid fluctuates with changes in temperature and the like. Therefore, in the above-described measuring method, if the temperature changes, the range in which N interference fringes occur also changes, and the thickness of the sample in that portion must be measured each time. Further, if the refractive index distribution of the lens is not uniform, irregularly shaped interference fringes are generated, and it is difficult to interpret N fringes. Therefore, in the measurement of the refractive index in such a case, there is a drawback that quantitative interpretation is difficult. In addition, it is difficult to automate the measurement.

The present invention eliminates such conventional drawbacks, the refractive index and the refractive index distribution can be measured without destroying an object whose shape and refractive index are unknown, and the quantitative interpretation is easy. An object of the present invention is to provide a refractive index measuring method which is easy to automate the measurement.

[Means for Solving the Problems] In order to achieve the above object, the refractive index measuring method of the present invention comprises a sample having a known refractive index and shape, and a test object having an unknown refractive index and shape. Dip in the matching liquid of No. 1 and allow coherent light to pass through them, superimpose the transmitted light wave with the reference light wave to generate interference fringes, and output the intensity distribution of the interference fringes generated by the light wave transmitted through the sample. The refractive index of the first matching liquid is obtained from the output, the intensity distribution of the interference fringes generated by the light wave that has passed through the test object is output, and the first polynomial representing the interference fringes is output from the output. Then, the sample and the test object are dipped in a second matching liquid whose refractive index is slightly different from that of the first matching liquid, and the coherent light is transmitted through these liquids, and the transmitted light wave is transmitted. Superimposition with reference light wave Interference fringes are generated, and the intensity distribution of the interference fringes generated by the light wave that has passed through the sample is output, the refractive index of the second matching liquid is obtained from the output, and the light wave that has passed through the test object is used. The intensity distribution of the generated interference fringes is output, the second polynomial representing the interference fringes is obtained from the output, and the refractive index of the first and second matching liquids and the first and second
The shape of the object to be inspected is obtained from the polynomial of

[Operation] FIG. 9 and FIG. 10 show the measurement principle of the refractive index measuring method of the present invention. x, y, z are coordinates.

First, when a plane wave of wavelength λ is transmitted through a test object immersed in a matching liquid whose refractive index n _m is almost equal to the refractive index n _{t of the} test object, the interference fringes obtained by the transmitted wave and the reference wave. W ₀
Consider (x, y).

If the shape of each surface of the object is I surface: Z ₁ = S ₁ (x, y) II surface: Z ₂ = S ₂ (x, y), and the center wall thickness is d, the amount of sag on both surfaces Total Sag (x,
y) is Sag (x, y) = S ₁ (x, y) + S ₂ (x, y) (1).

On the other hand, if the refractive index n _t (x, y) is separated into the average refractive index n _t0 and the refractive index distribution Δn _t (x, y), W _o (x, y) = Sag (x, y) · [ _{n t0 -n m] + [d} -Sag (x, y)] Δn t (x, y) ... (2) (2) by measuring the refractive index n _m of the matching liquid from the equation,
W ₀ (x, y) is a function of only n _t0 and Δn _t (x, y),
Generally, these two parameters cannot be obtained separately.

Now, if the above formula (2) is expanded using a Zernike polynomial that is generally used in the wavefront aberration expansion formula, then W _o (x, y) = Sag (x, y) ・ [n _t0 −n _m ] + [d−Sag (x, y)] Δn _t (x, y) = C ₁ + C ₂ ρcos + C ₃ ρsin + C ₄ (2ρ ² −1) + C ₅ ρ ² cos ² + ...

C ₂ cos and C ₃ ρ sin are tilt terms, C ₄ (2ρ ² −1) is a defocus term (W ₂ ), C ₅ ρ ₂ cos ² + ... Is an aberration term (W).

Then, since [n _t0 −n _m ] ≈ 0, Sag (x, y) · [n
_t0 −n _m ] can be approximated by a quadratic function, and is approximately equal to the defocus term.

FIG. 11 shows that one surface is a spherical surface (radius of curvature r), the other surface is a flat surface (radius of curvature ∞), the diameter is D, and there are various R numbers (R = r / D) with no refractive index distribution. Considering the test object, it was assumed that the matching solution was prepared so that the test object could have three stripes (W ₀ = 3λ) and one stripe (W ₀ = 1λ). In this case, the value of the aberration term (ΔW) is shown. If the reproducibility of fringe reading is λ / 25 in Rms, R> 0.7 even when the number of fringes is three.

Therefore, most of the R-number test objects have fringe reading reproducibility or less, indicating that the observed interference fringe component is represented only by the defocus term.

Therefore, [n _t0 −n _m ] is obtained from the defocus term of the read fringe W ₀ (x, y), and Δn is obtained from the aberration term W.
_{The t} (x, y) is obtained, and the two parameters can be separated. That is, (Se ₁ and Se ₂ are maximum Sag amounts on both sides of the test object as shown in FIG. 9.) Therefore, if the Sag amount, that is, the shape of the test object is known, the refractive index of the test object is determined. The distribution can be obtained from the aberration term of the polynomial, and if the refractive index of the matching liquid is known, the average refractive index of the test object can be obtained from the defocus term of the polynomial.

Therefore, in the present invention, at the time of measurement, the first and second matching liquids having slightly different refractive indexes are used, and the Sag amount of the test object is first obtained from the interference fringe analysis in each case. .

That is, the refractive indices of the first and second matching liquids are set to be n _m1 , n _m2
And the interference fringes generated when the first and second matching liquids are used are W ₀₁ and W ₀₂ , W ₀₁ (x, y) = Sag (x, y) · [n _t0 −n _m1 ] + [D−Sag (x, y)] Δn _t (x, y) (3) W ₀₂ (x, y) = Sag (x, y) · [n _t0 −n _m2 ] + [d−Sag (x , y)] Δn _t (x, y) (4) Therefore, from (3)-(4), Then, if the refractive indices n _m1 and n _m2 of each matching liquid are obtained,
The Sag amount of the test object can be obtained from the equation (5).

The refractive index of the matching liquid may be obtained from the known refractive index and shape of the sample.

[Example] FIG. 1 shows a measuring apparatus used in the present invention, and this apparatus is basically a Mach-Zehnder interferometer. Reference numeral 1 denotes a coherent light source that emits coherent light (wavelength λ), for example, a He-Ne laser light source. The light beam emitted from the coherent light source 1 is expanded by the beam expander lens 2,
The collimator lens 3 forms a parallel light beam. 4 is the first
The light flux reflected by the half mirror 4 is further reflected by the movable mirror 5 and transmitted through the transparent container 6. The movable mirror 5 can arbitrarily finely move (tilt) its angle.

The transparent container 6 is formed of glass without distortion.
Reference numeral 7 denotes an openable / closable lid. In the transparent container 6, the material of the test lens 10 is polymethyl methacrylate (acryl).
In the case of (1), for example, a matching liquid 8 in which dimethyl silicone oil and phenylmethyl silicone oil are mixed is contained.

In the matching liquid 8, as shown in FIG.
A glass sample 9 having a known refractive index ng and a shape (θ, L), and a lens 10 to be tested whose refractive index n _t and a shape (d, Sag (x, y)) are unknown.
And are arranged in parallel and perpendicular to the transmitted light flux.
The lens 10 to be inspected is generally a plastic lens such as polymethylmethacrylate (acrylic), but may be a lens made of glass or other material.

The light beam transmitted through the first half mirror 4 is reflected by the first fixed mirror 11 and then further reflected by the second half mirror 12.
Are superimposed on the light wave which has been reflected by the lens 10 and passed through the lens 10 to be inspected or the glass sample 9. Then, an interference fringe generated by the overlap of the two light waves forms an image on the surface of the imaging element 14 by the first imaging lens 13.

The first imaging lens 13 and the imaging element 14 are provided so as to be integrally movable in the vertical direction in the figure. Therefore, in FIG. 1, the first imaging lens
Although the lens 13 faces the lens 10 to be measured, the first imaging lens 13 may face the glass sample 9 as shown in FIG.

Returning to FIG. 1, the imaging element 14 is formed of, for example, 50 × 50 independent photoelectric elements. An AD converter 15, a digital operation circuit 16, and a display device 17 are sequentially connected to the output terminal. Further, the arithmetic circuit 16 is sequentially connected with a memory 18 for storing data necessary for the arithmetic operation and an input circuit 19 for inputting known data. Note that the arithmetic circuit 16 can be a microcomputer or other arithmetic device.

Reference numeral 20 denotes an observation device for observing the state in the transparent container 6, and includes a second fixed mirror 21 provided to face the second half mirror 12, a second imaging lens 22, It is composed of an imaging device 23 and a television monitor 24 provided at the image forming position.

In order to measure the refractive index of the lens 10 to be measured by the measuring method of the present invention, first, known data (ng, θ, L) regarding the glass sample 9 is input from the input circuit 19 to the memory 18 and stored. .

Next, the refractive index of the matching liquid 8 is adjusted. This adjustment is performed while watching the television monitor 24 so that the number of interference fringes generated by the light wave that has passed through the lens 10 to be inspected is, for example, three or less. The interference fringes may be reduced to one or less and disappear. Specifically, with the lid 7 of the transparent container 6 removed, one of the two types of silicone oil forming the matching liquid 8 is dropped into the container 6 with a dropper or the like, and the matching liquid 8 is stirred and mixed. Good. The first matching liquid of the present invention has the refractive index n _m1 thus determined.

Next, as shown in FIG.
Is made to face the glass sample 9. Then, as shown in FIG. 4, an interference fringe 30 generated by an overlap between the light wave transmitted through the glass sample 9 and the reference light wave forms an image on the image sensor 14. Then, the spatial frequency F _{1 of the} stripe is calculated in the arithmetic circuit 16 by the output from the image sensor 14 at that time. This can be done with the well-known Discrete Fourier Transform (DFT), but faster Fast Fourier Transform (FFT)
Good.

In this case, from the output on the line segment 31 which is perpendicular to the interference fringes 30 on the image pickup device 14 as shown in FIG.
An intensity distribution of brightness in a substantially sinusoidal shape as shown in the figure is calculated. Then, the spatial frequency F ₁ of the interference fringes is calculated from the intensity distribution by the FFT, and the refractive index n _m1 of the first matching liquid 8 is obtained from the calculated value.

That is, since F ₁ = k ₁ / L (n _m1 −ng) L · tan θ = λk _1, it can be calculated by n _m1 = ng + λ · F ₁ / tan θ. Then, the value of n _m1 is stored in the memory 18.

Next, as shown in FIG. 1, the first imaging lens 13
Is opposed to the lens 10 to be inspected. Then, the interference fringes 40 generated by the superposition of the light wave that has passed through the lens 10 to be inspected and the reference light wave form an image on the image sensor 14, as shown in FIG. The output from the image sensor 14 at that time is calculated by the arithmetic circuit 16
First, a high-precision fringe analysis is performed. This analysis is performed by, for example, a known spatial fringe scanning method by turning the movable mirror 5 by a slight angle to give a tilt to the stripe. Then, the phase is determined and subsequently expanded in the arithmetic circuit 16 into the first polynomial W ₀₁ (x, y). In the present embodiment, for example, the Zernike polynomial is expanded and stored in the memory 18.

Next, the mixing ratio of the matching liquid 8 is slightly changed. Also in this case, one of the two types of silicone oil that forms the matching liquid 8 is dropped into the container 6 with a dropper or the like, and the mixture is stirred and mixed. The second matching liquid of the present invention has the determined refractive index _nm2 . In this case, if the refractive index n _m1 of the first matching liquid is slightly larger than the refractive index n _{t of the} lens 10 to be measured, the refractive index n _m2 of the second matching liquid is adjusted to be slightly smaller than n _t. , N
_{If m1} is slightly smaller than n _t , then n _m2 should be adjusted slightly larger than n _t .

Next, in exactly the same manner as in the case of using the first matching liquid described above, the refractive index n _m2 of the second matching liquid is calculated from the interference fringes generated by the overlapping of the light wave transmitted through the glass sample 9 and the reference light wave. And stores the value in the memory 18.

Next, in the same manner as in the case of using the above-mentioned first matching liquid, interference fringes are generated by the superposition of the light wave transmitted through the lens 10 to be inspected and the reference light wave. FIG. 8 exemplifies the interference fringes 50 imaged on the image pickup device 14 at that time. Then, from the output of the image pickup device 14 at that time, the interference fringes are developed into the second polynomial W ₀₂ (x, y) in the arithmetic circuit 16. Then, the defocus term and the aberration term of this polynomial are stored in the memory 18.

Next, first, from the difference between the first and second polynomials W ₀₁ and W _{02 and} the difference between the refractive indices n _m1 and n _m2 of the first and second matching liquids,
The Sag amount (that is, shape) of the lens to be inspected, Ask as.

Then, the maximum Sag amount (Se ₁ + Se ₂ ) is obtained, the refractive index n _m2 of the second matching liquid is read from the memory 18, and the average refractive index n _{t0 of the} lens to be inspected 10 is read from the defocus term of the second polynomial. To And outputs the result to the display device 17 for display.

The thickness [d-Sag (x, y)] of each portion of the lens 10 to be inspected is read from the memory 18, and the refractive index distribution Δn of the lens 10 to be inspected is determined from the aberration term (W) of the second polynomial. (X, y)
To And outputs the result to the display device 17 for display.

In the above embodiment, the defocus term and the aberration term of the second polynomial are stored in the memory 18 and used for the measurement analysis. However, the first polynomial is used instead of the second polynomial. Good. In that case, the average refractive index of the lens 10 to be inspected
n _t0 is Is obtained as n _m1 is the refractive index of the first matching liquid.

[Effects of the Invention] According to the refractive index measuring method of the present invention, since the test object is only immersed in the matching liquid, it is not necessary to destroy the test object during the measurement. Moreover, by extracting the defocus term of the polynomial representing the interference fringes from the output of the intensity distribution of the interference fringes, the average refractive index of the object whose refractive index and shape are unknown can be obtained. Therefore, it has an excellent effect that it can be quantitatively determined, and therefore automatic analysis and the like can be easily performed.

[Brief description of the drawings]

1 to 3 are schematic diagrams showing an example of a measuring apparatus for performing the measurement according to the present invention, and FIGS. 4 to 6 are schematic diagrams showing a procedure for obtaining the refractive index of a matching liquid, FIG. 7 and FIG. 8th
FIG. 9 is a schematic diagram showing interference fringes generated on the surface of an image pickup device by a light wave transmitted through a lens to be inspected, FIGS. 9 and 10 are schematic diagrams illustrating the measurement principle of the present invention, and FIG. It is a diagram explaining the measurement accuracy based on the measurement principle.

Claims (3)

(57) [Claims] 1. A sample having a known refractive index and shape and an object having an unknown refractive index and shape are dipped in a first matching liquid to allow coherent light to pass therethrough, and the transmitted light wave is referred to. An interference fringe is generated by superimposing it on the light wave, the intensity distribution of the interference fringe generated by the light wave transmitted through the sample is output, the refractive index of the first matching liquid is obtained from the output, and the interference is transmitted through the test object. The intensity distribution of the interference fringes generated by the generated light wave is output, the first polynomial representing the interference fringe is obtained from the output, and then the sample and the test object are matched to each other with the first matching index of refraction. The second matching liquid, which is slightly different from the liquid, is soaked in the second matching liquid, the coherent light is transmitted therethrough, the transmitted light wave is superposed on the reference light wave to generate interference fringes, and the interference fringes caused by the light wave transmitted through the sample. Strength of The cloth is output, the refractive index of the second matching liquid is obtained from the output, and the intensity distribution of the interference fringes generated by the light wave transmitted through the test object is output, and the interference fringe is represented from the output. The second polynomial is obtained and the refractive index of the first and second matching liquids and the first
And a second polynomial, the shape of the object to be inspected is obtained. 2. The defocus term and the aberration term of the first or second polynomial are separated, and the object to be inspected is determined from the defocus term and the refractive index of the first or second matching liquid. The refractive index measuring method according to claim 1, wherein the average refractive index is obtained. 3. The refractive index according to claim 1, wherein the defocus term and the aberration term of the first or second polynomial are separated, and the refractive index distribution of the object to be examined is obtained from the aberration term. Measuring method.