JP2015010920A - Refractive index measuring method, refractive index measuring apparatus, and optical element manufacturing method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To measure a phase refractive index of a test object with high accuracy.
A phase of a test object 80 is obtained using an interference signal obtained by dividing light from a light source 10 into test light and reference light, and causing interference between the test light transmitted through the test object 80 and the reference light. Measure the refractive index. Obtaining the phase refractive index of the reference specimen, calculating a first physical quantity that is a function of the phase refractive index of the specimen 80, and using the first physical quantity and the phase refractive index of the reference specimen The phase refractive index of the object 80 is calculated, and a second physical quantity that is a function of the calculated phase refractive index of the test object 80 is calculated. The phase refractive index of the reference specimen is changed so that the difference between the first physical quantity and the second physical quantity is small, and the phase refractive index of the specimen 80 is changed using the changed phase refractive index of the reference specimen. Is recalculated.
[Selection] Figure 2

Description

  The present invention relates to a refractive index measurement method and a refractive index measurement device, and is particularly useful for measuring the refractive index of an optical element manufactured by molding.

  The refractive index of the mold lens varies depending on the molding conditions. The refractive index of the lens after molding is generally measured by the minimum deflection angle method or the V block method after processing into a prism shape. This processing work takes time and cost. Furthermore, the refractive index of the lens after molding changes due to stress release during processing. Therefore, a technique for measuring the refractive index of the molded lens in a nondestructive manner is necessary.

  The refractive index includes a phase refractive index relating to a phase velocity which is a moving velocity of the light equiphase surface, and a group refractive index relating to a moving velocity of light energy (moving velocity of wave packet).

  Non-Patent Document 1 proposes a method for calculating a phase refractive index by fitting an interference signal in a spectral region using a function of wavelength. Non-Patent Document 2 proposes a method of converting a group refractive index into a phase refractive index using statistical data regarding the refractive index of a large number of glasses.

H. Delbarre, C.I. Przygodzki, M .; Tassou, D.M. Boucher, “High-precise index measurement in anisotropical crystals using white-light spectral interferometry.” Applied Physics B, 2000, vol. 70, p. 45-51. J. et al. R. Rogers, M.M. D. Hopler, "Conversion of group refractive index to phase refractive index." Opt. Soc. Am. A, 1988, Vol. 5, no. 10, p. 1595-1600.

  In the method disclosed in Non-Patent Document 1, since the offset term of the phase of the interference signal (a term that is an integer multiple of 2π) is an unknown number, the fitting accuracy is low. In the method disclosed in Non-Patent Document 2, since the refractive index correction term used when converting the group refractive index to the phase refractive index is different from the refractive index correction term of the test object, an error in conversion to the phase refractive index. Will occur.

  An object of the present invention is to provide a refractive index measuring method and a refractive index measuring apparatus capable of measuring the phase refractive index of a test object with high accuracy.

  The refractive index measurement method of the present invention divides light from a light source into test light and reference light, causes the test light to enter the test object, and passes the test light and the reference light through the test object. A refractive index measurement method for measuring a phase refractive index of the test object using an interference signal obtained by interfering with a reference object, wherein an acquisition step for acquiring a phase refractive index of a reference test object is used, and the interference signal is used. A first calculation step of calculating a first physical quantity that is a function of the phase refractive index of the test object, and the phase of the test object using the first physical quantity and the phase refractive index of the reference test object. A second calculating step for calculating a refractive index; a third calculating step for calculating a second physical quantity that is a function of the phase refractive index of the test object calculated in the second calculating step; and the first physical quantity. And the phase bending of the reference specimen so that the difference between the second physical quantity and the second physical quantity is small. Change rates, characterized by having a a recalculation step of re-calculating the phase index of the test object using the phase index of the modified the reference test object.

  The method of manufacturing an optical element of the present invention includes a step of molding an optical element, and a step of evaluating the molded optical element by measuring the refractive index of the optical element using the refractive index measurement method. It is characterized by having.

  The refractive index measuring apparatus of the present invention splits light from a light source and light from the light source into test light and reference light, causes the test light to enter the test object, and transmits the test light through the test object. Interference optical system for causing light and reference light to interfere, detection means for detecting interference light between the reference light and the test light, and phase refraction of the test object using an interference signal output from the detection means A refractive index measuring device comprising a calculating means for calculating a refractive index, wherein the calculating means obtains a phase refractive index of a reference test object, and uses the interference signal as a function of the phase refractive index of the test object. A first physical quantity is calculated, the phase refractive index of the test object is calculated using the first physical quantity and the phase refractive index of the reference test object, and the calculated phase refractive index of the test object is calculated. The second physical quantity that is a function of is calculated, and the difference between the first physical quantity and the second physical quantity is reduced. Change the phase index of sea urchin the reference test object, it is characterized by re-calculating the phase index of the test object using the phase index of the modified the reference test object.

  ADVANTAGE OF THE INVENTION According to this invention, the refractive index measuring method and refractive index measuring apparatus which can measure the phase refractive index of a test object with high precision can be provided.

It is a block diagram of the refractive index measuring device of Example 1 of the present invention. It is a flowchart which shows the calculation procedure of the phase refractive index of the test object in the refractive index measuring apparatus of Example 1 of this invention. It is a figure which shows the interference signal obtained with the detector of the refractive index measuring device of Example 1 of this invention. It is a figure which shows the comparison of the 1st physical quantity of Example 1 of this invention, and a 2nd physical quantity. It is a block diagram of the refractive index measuring device of Example 2 of the present invention. It is a block diagram of the refractive index measuring device of Example 3 of the present invention. It is a figure which shows the manufacturing process of the manufacturing method of the optical element of Example 4 of this invention.

  Embodiments of the present invention will be described below with reference to the accompanying drawings.

  FIG. 1 is a block diagram of the refractive index measuring apparatus according to the first embodiment. The refractive index measuring apparatus of the present embodiment is composed of a Mach-Zehnder interferometer. In this embodiment, the test object is a lens having negative refractive power (reciprocal of focal length). Since the refractive index measuring apparatus measures the refractive index of the test object, the test object may be a lens or a flat plate, and any refractive optical element may be used.

  The refractive index measuring device includes a light source 10, an interference optical system, a container 60 that can accommodate a medium 70 and a test object 80, a detector 90, and a computer 100, and measures the refractive index of the test object 80.

  The light source 10 is a light source having a wide wavelength band (for example, a supercontinuum light source). The interference optical system divides the light from the light source 10 into light that passes through the test object (test light) and light that does not pass through the test object (reference light), and superimposes the test light and the reference light. Then, the interference light is guided to the detector 90. The interference optical system according to the first embodiment includes a plurality of beam splitters 20 and 21 and a plurality of mirrors 30, 31, 40, 41, 50 and 51.

  The beam splitters 20 and 21 are constituted by, for example, cube beam splitters. The beam splitter 20 transmits part of the light from the light source 10 and reflects the rest at the joint surface 20a of the two right-angle prisms. The light transmitted through the joint surface 20a is reference light, and the light reflected by the joint surface 20a is test light. The beam splitter 21 reflects part of the reference light and transmits part of the test light at the joint surface 21a of the right-angle prism. As a result, the reference light and the test light interfere to form interference light, and the interference light is emitted to the detection unit 90.

  The container 60 contains a medium 70 (for example, water or oil) and a test object 80. It is preferable that the optical path length of the reference light in the container and the optical path length of the test light coincide with each other in a state where the test object 80 is not arranged in the container. Therefore, it is desirable that the side surface (for example, glass) of the container 60 has a uniform thickness and refractive index, and both side surfaces of the container 60 are parallel. If the medium 70 is air, the container 60 may not be provided.

  The refractive index of the medium 70 is calculated by a medium refractive index calculation unit (not shown). The medium refractive index calculating means includes, for example, a temperature measuring means that measures the temperature of the medium and a computer that converts the measured temperature into a medium refractive index. Alternatively, the medium refractive index calculating means includes a glass prism having a known refractive index and shape, a wavefront measuring sensor (wavefront measuring means) for measuring a transmitted wavefront of the glass prism disposed in the medium, and a medium based on the transmitted wavefront and shape. It may be composed of a computer that calculates the refractive index.

  The mirrors 40 and 41 are, for example, prism type mirrors. The mirrors 50 and 51 are, for example, corner cube reflectors. The mirror 51 has a drive mechanism in the direction of the arrow in FIG. The drive mechanism of the mirror 51 is composed of, for example, a stage with a wide drive range and a piezo element with high drive resolution. The driving amount of the mirror 51 is measured by a length measuring device (not shown) (for example, a laser length measuring device or an encoder). The drive of the mirror 51 is controlled by the computer 100. The optical path length difference between the test light and the reference light can be adjusted by the drive mechanism of the mirror 51.

  The detector 90 is a detecting unit that splits interference light from the beam splitter 21, detects the interference light intensity as a function of wavelength (frequency), and outputs an interference signal, and includes a spectrometer.

  The computer 100 functions as a calculation unit that calculates the refractive index of the test object from the interference signal output from the detector 90, and also functions as a control unit that controls the driving amount of the mirror 51. The computer 100 includes a CPU and the like. Yes. However, the calculation means for calculating the refractive index of the test object from the interference signal output from the detector 90 and the control means for controlling the drive amount of the mirror 51 and the temperature of the medium 70 can be configured by different computers. .

  The interference optical system is adjusted so that the optical path lengths of the test light and the reference light are equal in a state where the test object 80 is not disposed in the container. The adjustment method is as follows.

In the refractive index measurement apparatus of FIG. 1, an interference signal between the reference light and the test light is acquired in a state where the test object 80 is not placed on the optical path of the test light. At this time, the phase difference φ ₀ (λ) and the interference intensity I ₀ (λ) between the reference light and the test light are expressed by Equation 1.

Where λ is the wavelength in the air, Δ ₀ is the difference between the optical path lengths of the test light and the reference light, I ₀ is the sum of the intensity of the test light and the reference light, and γ is the visibility (visibility). From Equation 1, when Δ ₀ is not zero, the interference intensity I ₀ (λ) is a vibration function. Therefore, in order to make the optical path lengths of the test light and the reference light equal, the mirror 51 may be driven to a position where the interference signal does not become a vibration function. At this time, delta ₀ becomes zero.

Here, the case where the optical path lengths of the test light and the reference light are adjusted to be equal (Δ ₀ = 0) has been described, but how much the current position of the mirror 51 is shifted from Δ ₀ = 0. If it is known, it is not necessary to make the optical path lengths of the test light and the reference light equal. The driving amount of the mirror 51 from the position where the optical path lengths of the test light and the reference light are equal (Δ ₀ = 0) can be measured by a length measuring device (not shown) (for example, a laser length measuring device or an encoder).

  FIG. 2 is a flowchart showing a procedure for calculating the phase refractive index of the test object 80, and “S” is an abbreviation for Step.

  First, the phase refractive index of the reference specimen is acquired (acquisition step S10). The reference specimen means a specimen whose phase refractive index is known in the wavelength range measured by the detector 90. The acquired phase refractive index may be discrete data of the phase refractive index corresponding to each wavelength, or may be a coefficient of a dispersion formula (for example, a Cellmeier dispersion formula or a Cauchy dispersion formula).

  The reference specimen is a glass material having a refractive index close to the refractive index of the specimen (for example, the difference between the reference specimen and the specimen is a refractive index difference of less than 0.05 and an Abbe number difference of 5). %) Is desirable. For example, a glass material that is a base material of the test object may be selected as the reference test object. At that time, the value of the phase refractive index of the base material provided by the glass material manufacturer can be used as the phase refractive index of the reference specimen.

  The phase refractive index of the reference test object is stored in, for example, the computer 100 and can be acquired simply by inputting the glass material name. At this time, the computer 100 serves as acquisition means for acquiring the phase refractive index of the reference test object.

  When the glass material of the test object is unknown, the phase refractive index of a sample made of the same glass material as the test object can be used as the phase refractive index of the reference test object. The phase refractive index of the sample may be measured by processing measurement (processing into a prism shape and measuring by the minimum deflection angle method or the V block method). Since the amount of change in the refractive index due to stress release during processing is small, even the phase refractive index of the sample after processing can be used as the phase refractive index of the reference specimen. The phase refractive index of the processed sample can be the phase refractive index of the reference specimen of all specimens as long as the specimen is made of the same glass material. Machining and measurement takes time and effort, but only needs to be performed once.

Next, a first physical quantity that is a function of the phase refractive index of the test object is calculated from the interference signal between the test light transmitted through the test object and the reference light (first calculation step S20). The first physical quantity may be any physical quantity as long as it is a function of the phase refractive index of the test object. For example, the phase difference between the test light and the reference light, the slope of the phase difference between the test light and the reference light (the differential of the phase difference), the group refractive index of the test object, etc. are all in the first physical quantity. Can be. In this embodiment, the phase difference φ ₁ (λ) between the test light and the reference light is selected as the first physical quantity.

When the test object is placed on the optical path of the test light, the interference signal in the spectral region measured by the detector 90 in FIG. 1 is as shown in FIG. The phase difference φ ₁ (λ) between the test light and the reference light is expressed by Equation 2.

Here, n ^sample (λ) is the phase refractive index of the test object, n ^medium (λ) is the phase refractive index of the medium, and L is the geometric thickness of the test object. Λ _{0 in} FIG. 3 indicates a wavelength at which the phase difference φ ₁ (λ) takes an extreme value. Since the period of the interference signal becomes longer at wavelengths near λ ₀ , the interference signal is easy to measure. On the other hand, since the period of the interference signal becomes shorter at wavelengths away from λ ₀ , the interference signal may become too dense to be decomposed. If λ ₀ is out of the measurement range, the mirror 51 may be driven to adjust Δ ₀ .

The phase difference φ ₁ (λ) can be calculated using, for example, the following phase shift method. An interference signal is acquired while driving the mirror 51 minutely. The interference intensity I _k (λ) when the phase shift amount (= drive amount × 2π / λ) of the mirror 51 is δ _k (k = 0, 1,..., M−1) is expressed by Equation 3. .

The phase difference φ ₁ (λ), which is the first physical quantity, is calculated by Equation 4 using the phase shift amount δ _k and the interference intensity I _k (λ). In order to improve the calculation accuracy of the phase difference φ ₁ (λ), the phase shift amount δ _k should be made as small as possible and the number of drive steps M should be made as large as possible. The calculated phase difference φ ₁ (λ) is convolved with 2π. Therefore, an operation (unwrapping) for connecting 2π phase jumps is necessary.

  Next, the phase refractive index of the test object 80 is calculated using the first physical quantity and the phase refractive index of the reference test object (second calculation step S30). The calculation method of the phase refractive index of the test object 80 is as follows.

The phase difference φ ₁ (λ) (first physical quantity) obtained by the phase shift method has arbitraryness (unknown offset term) that is an integer multiple of 2π. In order to remove this arbitrary property, the gradient dφ ₁ (λ) / dλ with respect to the wavelength of the phase difference is calculated. The inclination related to the wavelength of the phase difference corresponds to a first-order differential amount related to the wavelength of the phase difference. Since the phase difference φ ₁ (λ) is discrete data, the rate of change between the wavelength data is actually calculated. The gradient dφ ₁ (λ) / dλ relating to the wavelength of the phase difference is expressed by Equation 5.

However, _ng ^sample (λ) is the group refractive index of the test object, and _ng ^medium (λ) is the group refractive index of the medium. In general, the operation of calculating the differential amount of data amplifies the influence of noise. In order to reduce the influence of noise, the derivative amount may be calculated after smoothing the original data. Alternatively, the differential data itself may be smoothed.

Next, the group refractive index N _g (λ) of the reference specimen is calculated using Equation 6 from the phase refractive index N _p (λ) of the reference specimen. In this embodiment, the Cauchy dispersion formula is used as the phase refractive index of the reference specimen. C _k (k = 1, 2,..., 6) is a coefficient of Cauchy's dispersion formula.

Then, the relationship between the group refractive index and the phase refractive index is calculated. The relationship between the group refractive index and the phase refractive index is a relationship that can be understood when one is understood. For example, the relationship between the group refractive index N _g (λ) and the phase refractive index N _p (λ), This is the relationship between the ratio of the group refractive index N _g (λ) and the phase refractive index N _p (λ).

  The reason for calculating the relationship between the group refractive index and the phase refractive index of the reference specimen is that the phase refractive index cannot be uniquely calculated from the group refractive index. Formula 7 is a formula for calculating the phase refractive index from the group refractive index. As shown in Equation 7, the phase refractive index has an arbitrary integration constant C.

The gradient dφ ₁ (λ) / dλ relating to the wavelength of the phase difference expressed by Equation 5 is a function of the group refractive index _ng ^sample (λ). When calculating the phase refractive index n ^sample (λ) from dφ ₁ (λ) / dλ, the group refractive index n _g ^sample (λ) is present in the calculation process. It is not calculated uniquely. Therefore, the phase refractive index n ^sample (λ) of the test object is calculated using the relationship between the group refractive index and the phase refractive index of the reference test object. For example, when the relationship between the difference in the group refractive index N _g (λ) and the phase refractive index N _p (λ) of the reference specimen is used, Equation 5 is transformed into Equation 8.

In Expression 8, the phase refractive index n ^sample (λ) of the test object is known. Therefore, if equation 8 is fitted assuming a dispersion equation of phase refractive index n ^sample (λ) (for example, a Cermeier dispersion equation such as equation 9), coefficients A ₁ , A ₂ , A ₃ , B ₁ , B ₂ , B ₃ are calculated. That is, a dispersion formula of the phase refractive index n ^sample (λ) is obtained. If the geometric thickness L of the test object is unknown, the geometric thickness L may be fitted as a parameter. Alternatively, as the geometric thickness L of the test object, for example, a test object design value may be used.

As described above, the phase refractive index of the test object is calculated using the first physical quantity (phase difference φ ₁ (λ)) and the phase refractive index of the reference test object (second calculation step S30). .

  In the phase refractive index of the test object calculated in the second calculation step S30, the relationship between the group refractive index and the phase refractive index of the reference test object is equal to the relationship between the group refractive index and the phase refractive index of the test object. Calculated under assumptions. However, since the relationship between the group refractive index and the phase refractive index of the reference specimen is actually different from the relationship between the group refractive index and the phase refractive index of the specimen, the calculated phase refractive index of the specimen is Includes errors (hereinafter referred to as dispersion errors). Therefore, it is necessary to reduce the dispersion error as follows.

A second physical quantity φ ₂ (λ) that is a function of the phase refractive index n ^sample (λ) of the test object calculated in the second calculation step S30 is calculated (third calculation step S40). The second physical quantity φ ₂ (λ) is a physical quantity of the same dimension corresponding to the first physical quantity φ ₁ (λ) (phase difference in this embodiment). The second physical quantity φ ₂ (λ) is obtained by using the phase refractive index n ^sample (λ of the test object calculated in the second calculation step S30 without using the relationship between the group refractive index and the phase refractive index of the reference test object. ) And Equation 2. Since the first physical quantity φ ₁ (λ) includes an offset that is an integer multiple of 2π, the second physical quantity φ ₂ (λ) must also include an offset that is an integer multiple of 2π. The offset of the second physical quantity can be adjusted by, for example, comparing the extreme value with the first physical quantity and adding or subtracting an integer multiple of 2π.

Next, the first physical quantity φ ₁ (λ) is compared with the second physical quantity φ ₂ (λ) (S50). FIG. 4 is a diagram comparing the first physical quantity and the second physical quantity. If the dispersion error is zero, the first physical quantity matches the second physical quantity. The greater the variance error, the greater the difference between the first physical quantity and the second physical quantity. The phase refractive index calculation flow in FIG. 2 ends if this difference is small, and proceeds to step S60 if the difference is large.

  The boundary value that determines whether the difference between the first physical quantity and the second physical quantity is large or small depends on the accuracy of the refractive index to be obtained. For example, when the phase refractive index of the test object is 1.9, the phase refractive index of the medium is 1.6, the geometric thickness of the test object is 1 mm, and the wavelength is 633 nm, the phase refractive index of the test object is 0. When it is desired to obtain with accuracy of .0001 or less, the boundary value is 1 rad.

  When the difference between the first physical quantity and the second physical quantity is large, the phase refractive index of the reference test object is changed so that the difference becomes small (S60). As a method for changing the phase refractive index of the reference specimen, for example, there are the following methods.

Only coefficients _{C 1} to phase index formula 6 by a small amount .delta.C ₁ is changed, performs S40 from step S30. A change amount Δφ ₂ ^C1 (λ) of φ ₂ (λ) due to a change in the minute amount δC ₁ is calculated. Coefficients _{C 2, C 3, C 4} , C 5, the same operations as the coefficient _{C 1} with regard _{C 6} is performed, the amount of change in each of ^{_{φ 2 (λ) Δφ 2 C2}} (λ), Δφ 2 C3 (λ ), Δφ ₂ ^C4 (λ), Δφ ₂ ^C5 (λ), and Δφ ₂ ^C6 (λ). Coefficients χ ₁ , χ ₂ , χ ₃ , χ ₄ , χ ₅ , χ ₆ that best satisfy Equation 10 are obtained. The coefficient χ _k (k = 1, 2,..., 6) may be calculated using, for example, the least square method. As shown in Equation 11, the phase refractive index N _p (λ) of the reference specimen is changed.

Expression 10 is an expression for calculating how much the coefficients C ₁ to C ₆ change to reduce the difference between the first physical quantity and the second physical quantity. Formula 11 is a formula for changing the phase refractive index of the reference specimen of Formula 6 based on the result of Formula 10. As the phase refractive index of the reference specimen is changed, the relationship between the group refractive index and the phase refractive index of the reference specimen also changes.

The subsequent flow uses the first physical quantity and Equation 11 to recalculate the phase refractive index of the test object (S30), and the second physical quantity φ ₂ (λ that is a function of the recalculated phase refractive index. ) Is recalculated (S40), and it is confirmed that the difference between φ ₁ (λ) and φ ₂ (λ) is small (S50), and the process ends. If the difference is large in step S50, the flow proceeds to step S60 again. As described above, the phase refractive index of the reference specimen is changed so that the difference between the first physical quantity and the second physical quantity is small, and the specimen is used by using the phase refractive index of the changed reference specimen. The phase refractive index of 80 is recalculated (recalculation step).

  As a method for calculating the phase refractive index of the test object in the second calculation step S30, the following method may be used instead of the dispersion fitting method using Equations 8 and 9.

Since the group refractive index _ng ^sample (λ) of the test object is calculated by modifying Equation 5, the phase refractive index n ^sample (λ) can also be calculated as Equation 12. In Expression 12, the relationship between the group refractive index and the phase refractive index of the reference test object is expressed using a ratio relationship.

  The calculation method of the phase refractive index of the test object in the second calculation step S30 may be the following method.

  Assuming that a reference specimen having the same thickness L as the specimen is measured instead of the specimen, the slope dΦ (λ) / dλ relating to the wavelength of the phase difference with respect to the reference specimen is expressed by Equation 13. Can be calculated. dΦ (λ) / dλ can be actually measured by using the refractive index measurement device of this embodiment instead of calculating using Equation 13.

Using the relationship between the inclination dΦ (λ) / dλ and the phase refractive index N _p (λ) (difference relationship, ratio relationship, etc.) with respect to the wavelength of the phase difference, the phase refractive index n ^sample (λ) is Can be calculated.

This method uses the relationship between the phase refractive index and dΦ (λ) / dλ, which is a function of the group refractive index, instead of the relationship between the group refractive index and the phase refractive index of the reference specimen. As described above, the relationship linked to the phase refractive index may be other than dΦ (λ) / dλ as long as it is a function of the group refractive index (including the group refractive index itself). For example, the optical path length difference obtained by the formula deformed from Equation ^{_{13 (N g (λ) -n}} g medium (λ)) L-Δ0 and the group refractive index difference ^{_{N g (λ) -n g medium}} (λ) may be used.

  The physical quantity in this specification indicates an amount for comparing the magnitude of the dispersion error. In this embodiment, the phase difference is used as the physical quantity. However, it is not always necessary to use the phase difference, and it may be a function of the phase refractive index of the test object.

For example, the physical quantity can also be compared with the slope of the phase difference expressed by Equation 5 with respect to the wavelength. A function of the phase refractive index n ^sample (λ) obtained in the second calculation step S30 is dφ ₁ / dλ instead of the first physical quantity φ ₁ (λ), and is substituted for the second physical quantity φ ₂ (λ). Dφ ₂ / dλ.

The physical quantity may be the group refractive index itself instead of the phase difference. A substitute for the first physical quantity φ ₁ (λ) is the group refractive index _ng ^sample (λ) of the test object calculated by Expression 12, and a substitute for the second physical quantity φ ₂ (λ) is the second physical quantity φ ₂ (λ). The group refractive index is uniquely calculated from the phase refractive index n ^sample (λ) obtained in the calculation step S30.

  If the first physical quantity is a quantity that can be uniquely calculated from the measurement data, a phase difference can be substituted. For example, a quantity like Formula 15 obtained by transforming from Formula 5 can also be a physical quantity in the present invention.

  In step S60, the phase refractive index of the reference specimen is changed by adjusting the coefficient of the dispersion formula as in Expressions 10 and 11, but instead of adjusting the coefficient of the dispersion formula, The discrete data itself may be adjusted. A simple adjustment method is, for example, addition / subtraction of an offset component or a linear component.

  In this embodiment, the test object 80 is disposed in a medium 70 such as oil (a medium having a phase refractive index higher than that of air). The refractive index measurement method of the present invention can be realized even when the medium 70 is air. However, there is an advantage in reducing the refractive index difference between the test object 80 and the medium 70.

  There are mainly two advantages of reducing the refractive index difference. One advantage is that the effects of lens refraction can be reduced. Another advantage is that the influence of the geometric thickness error of the specimen can be reduced. As can be seen from Equation 2 and Equation 5, when the refractive index difference is small, the coefficient multiplied by the thickness of the test object is small. Therefore, the influence of the error of the specimen geometric thickness is also reduced.

In particular, at a specific wavelength where the group refractive index _ng ^sample (λ) of the test object is equal to the group refractive index _ng ^medium (λ) of the ^medium , the influence of the error in the geometric thickness of the test object becomes zero. . For this reason, the medium used when measuring the specimen having an unknown geometric thickness is preferably a medium having a group refractive index equal to the group refractive index of the specimen at a specific wavelength in the wavelength range to be measured.

  Since the refractive index distribution of the medium 70 is generated by the temperature distribution of the medium 70, an error occurs in the calculated refractive index of the test object. Therefore, it is desirable to control by the temperature adjustment mechanism (temperature adjustment means) so that the temperature distribution of the medium 70 does not occur. In addition, since the error due to the refractive index distribution of the medium 70 can be corrected if the amount of the refractive index distribution is known, it is desirable to have a wavefront measuring device (wavefront measuring means) for measuring the refractive index distribution of the medium 70.

  If the measurement is performed under two kinds of temperature conditions or two kinds of medium conditions instead of matching the group refractive indexes of the specimen and the medium, an error in the geometric thickness of the specimen can be removed.

  The method of removing the geometric thickness error under the two types of temperature conditions is as follows.

When the phase differences measured when the temperature of the test object is the first temperature T _A and the second temperature T _B are φ _1A (λ) and φ _1B (λ), Each optical path length difference is expressed by Equation 16.

Where dN _g / dT is the temperature coefficient of the refractive index of the test object, T ₀ is the reference temperature, _ngA ^medium (λ) is the group refractive index of the medium at the temperature T _A , and _ngB ^medium (λ) is the temperature T _B. Is the linear expansion coefficient of the test object, and is a known value. dN _g / dT is a temperature coefficient of the group refractive index, and is calculated from the temperature coefficient of the phase refractive index. When the geometric thickness L of the test object is removed from Expression 16, Expression 17 is obtained.

Equation 17 does not include the geometric thickness L of the test object and is not affected by the thickness error. If the group refractive index _ng ^sample (λ) of the test object obtained by Equation 17 is used instead of _ng ^sample (λ) obtained by Equation 12, the influence of the thickness error can be eliminated. At this time, the group refractive index _ng ^sample (λ) of the test object obtained by Expression 17 can be used as the first physical quantity. Note that the group refractive index _ng ^sample (λ) of the test object obtained by Expression 17 is a value at the reference temperature T ₀ .

The accuracy of calculation of the group refractive index _ng ^sample (λ) of the test object using Equation 17 increases as the denominator on the right side increases. In other words, the group index _n ^{g sample} _(λ) calculation accuracy is higher as the difference between the temperature _{T A} and _{T B} is large. Accordingly, the temperature _{T A} and _{T B} conditions the difference is greater are preferred.

The temperature coefficient dN _g / dT of the refractive index and the linear expansion coefficient α are assumed to be known, and are, for example, values of the base material provided by the glass material manufacturer. Strictly speaking, dN _g / dT and α of the test object 80 are different from the values of the base material, but there is no problem even if it is assumed to be equal to the value of the base material. The reason is as follows.

The reason is that even if the refractive index of the glass material changes slightly, the temperature coefficient and the linear expansion coefficient hardly change, and the group refractive index _ng ^sample (λ) of Equation 17 is the change in the temperature coefficient and the linear expansion coefficient. Because it is insensitive. Accordingly, it is only necessary that one set of temperature coefficient and linear expansion coefficient of a glass material having a refractive index close to that of the test object is known. Since the influence of the linear expansion coefficient on the group refractive index calculated by Expression 17 is particularly small, the expansion of the test object 80 may not be considered (that is, the linear expansion coefficient is zero).

The influence of the geometric thickness error of the test object can also be eliminated by using two types of medium conditions in which the test object is arranged in the first medium and the second medium having different refractive indexes. . The equation for removing the geometric thickness error under the two types of medium conditions is expressed by the equation of dN _g / dT = 0 and α = 0 in Equation 17. However, the group refractive index of the first medium is _ngA ^medium (λ), the group refractive index of the second medium is _ngB ^medium (λ), and the phase difference measured in each medium is φ _1A (λ), φ _1B (λ).

Similar to the method of removing the geometric thickness error caused by the two types of temperature conditions, the larger the denominator of the right side of Equation 17, the higher the accuracy of calculating the group refractive index _ng ^sample (λ). Therefore, it is desirable that the difference between the refractive index of the first medium and the refractive index of the second medium is large.

In this embodiment, the phase difference φ ₁ (λ) is measured by a combination of mechanical phase shift by the mirror 51 and spectroscopy by the detector 90. Instead, heterodyne interferometry may be used. When heterodyne interferometry is used, the interferometer, for example, arranges a spectroscope immediately after the light source and emits pseudo-monochromatic light, generates a frequency difference between the reference light and the test light by the acousto-optic device, and causes interference. The signal is measured with a detector such as a photodiode. Then, the phase difference φ ₁ (λ) is calculated at each wavelength while scanning the wavelength with a spectroscope.

  In this embodiment, a supercontinuum light source is used as the light source 10 having a wide wavelength band. Instead, a super luminescent diode (SLD), a halogen lamp, a short pulse laser, or the like may be used. When scanning the wavelength, a wavelength swept light source may be used instead of the combination of the broadband light source and the spectroscope.

  In the present embodiment, the configuration of the Mach-Zehnder interferometer is used, but the configuration of a Michelson interferometer may be used instead. In this embodiment, the refractive index and the phase difference are calculated as a function of wavelength, but may be calculated as a function of frequency instead.

  FIG. 5 is a block diagram of the refractive index measuring apparatus according to the second embodiment of the present invention. An interferometer that measures the refractive index of the medium 70 is added to the refractive index measurement apparatus of the first embodiment. The test object is a lens having a positive refractive power. In this embodiment, the test object is disposed in a medium (for example, oil) having a group refractive index equal to the group refractive index of the test object at a specific wavelength in the wavelength range to be measured. The same configurations as those in the first embodiment will be described with the same reference numerals.

  The light emitted from the light source 10 is split into transmitted light and reflected light by the beam splitter 22. The transmitted light travels to the interference optical system for measuring the refractive index of the test object 80, and the reflected light is guided to the interference optical system for measuring the refractive index of the medium 70. The reflected light is further divided into transmitted light (medium reference light) and reflected light (medium test light) by the beam splitter 23.

  The medium test light reflected by the beam splitter 23 is reflected by the mirrors 42 and 52, passes through the side surface of the container 60 and the medium 70, is reflected by the mirror 33, and reaches the beam splitter 24. The medium reference light transmitted through the beam splitter 23 is reflected by the mirrors 32, 43, and 53, then passes through the compensation plate 61 and reaches the beam splitter 24. The medium reference light and the medium test light that have reached the beam splitter 24 interfere with each other to form interference light, which is detected by the detection unit 91 configured by a spectroscope or the like. A signal detected by the detector 91 is sent to the computer 100.

  The compensation plate 61 plays a role of correcting the influence of refractive index dispersion due to the side surface of the container 60 and is made of the same material and the same thickness as the side surface of the container 60 (= thickness of the side surface of the container 60 × 2). The compensation plate 61 has an effect of equalizing the optical path length difference between the wavelengths of the medium test light and the medium reference light when the container 60 is empty.

  The mirror 53 has a drive mechanism similar to that of the mirror 51, and is driven in the direction of the arrow in FIG. The drive of the mirror 53 is controlled by the computer 100. The container 60 is provided with a temperature adjustment mechanism (not shown), and can increase and decrease the temperature of the medium, control the temperature distribution of the medium, and the like. The medium temperature is also controlled by the computer 100.

  The medium 70 has a group refractive index equal to that of the test object at a specific wavelength. In general, since the ultraviolet absorption band of oil is closer to visible light than the ultraviolet absorption band of glass material, the gradient of refractive index (refractive index dispersion) in the visible light region of oil is steeper than the gradient of glass material. Even in a high refractive index region where there is no practical phase refractive index matching oil, there is an oil that can match the group refractive index.

  The procedure for calculating the phase refractive index of the test object 80 of the present embodiment is as follows.

  First, the phase refractive index of the reference specimen is acquired (acquisition step S10), and the first physical quantity is calculated (first calculation step S20).

The phase difference between the test light and the reference light is expressed by Equation 2, and the slope of the phase difference with respect to the wavelength is expressed by Equation 5. The interference signal between the test light and the reference light is as shown in FIG. In FIG. 3, λ ₀ is the wavelength of the extreme value of the phase difference. In other words, λ ₀ is a wavelength at which the gradient with respect to the wavelength of the phase difference becomes zero. When Δ ₀ is zero, the wavelength at which dφ ₁ (λ) / dλ is zero is the wavelength where the group refractive index _ng ^sample (λ) of the test object is equal to the group refractive index _ng ^medium (λ) of the ^medium ( Specific wavelength). Therefore, if the wavelength at which the phase difference takes an extreme value is measured, the group refractive index of the medium 70 at that wavelength corresponds to the group refractive index of the test object 80.

The gradient dφ ^medium (λ) / dλ relating to the wavelengths of the phase difference φ ^medium (λ) and the phase difference φ ^medium (λ) between the medium test light and the medium reference light is expressed by Equation 18.

However, L ^tank is the distance between the side surfaces of the container 60 (the path length of the medium test light in the medium 70), which is a known amount. Since λ is the wavelength in air, the refractive index of air is built into the wavelength. Here, it is assumed that the phase refractive index of air is equal to the group refractive index of air.

The phase difference φ ^medium (λ) between the medium test light and the medium reference light is measured by a phase shift method using driving of the mirror 53. When formula 18 is transformed, the group refractive index _ng ^medium (λ) of the ^medium is obtained. A specific wavelength λ ₀ that takes the extreme value of the phase difference between the test light and the reference light is determined from the interference signal in FIG. 3, and the group refractive index of the test object at the wavelength λ ₀ is calculated from Equation 19.

When the temperatures of the medium 70 and the test object 80 change, the specific wavelength λ ₀ changes. Therefore, when the above measurement is repeated at a number of temperatures, the group refractive index _ng ^sample (λ) of the test object in a certain wavelength range is calculated. In the present embodiment, the group refractive index _ng ^sample (λ) of the test object can be used as the first physical quantity (first calculation step S20).

  Next, the phase refractive index of the test object 80 is calculated using the first physical quantity (group refractive index of the test object) and the phase refractive index of the reference test object (second calculation step S30). Then, the second physical quantity (group refractive index) that is a function of the phase refractive index of the test object 80 calculated in the second calculation step is uniquely calculated (third calculation step S40). Further, the second physical quantity is compared with the first physical quantity (S50).

  When the difference between the first physical quantity and the second physical quantity is large, the phase refractive index of the reference test object is changed so that the difference becomes small (S60). The phase refractive index of the test object to be obtained is obtained as the phase refractive index when the difference becomes small (recalculation step).

  FIG. 6 is a block diagram of the refractive index measuring apparatus according to the third embodiment of the present invention. The wavefront is measured using a two-dimensional sensor. In order to measure the refractive index of the medium, a glass prism having a known refractive index and shape is arranged on the optical path of the test light beam. The same configurations as those in the first and second embodiments will be described with the same reference numerals.

  The light emitted from the light source 10 is split by the spectroscope 95 and enters the pinhole 110 as pseudo-monochromatic light. The wavelength of the pseudo-monochromatic light incident on the pinhole 110 is controlled by the computer 100. The light that has passed through the pinhole 110 and becomes divergent light is collimated into parallel light by the collimator lens 120. The collimated light is split by the beam splitter 25 into transmitted light (reference light) and reflected light (test light).

  The reference light transmitted through the beam splitter 25 passes through the medium 70 in the container 60, is reflected by the mirror 31, and reaches the beam splitter 26. The mirror 31 has a drive mechanism in the direction of the arrow in FIG. 6 and is controlled by the computer 100.

  The test light reflected by the beam splitter 25 is reflected by the mirror 30 and enters the container 60 that houses the medium 70, the test object 80, and the glass prism 130. Part of the test light passes through the medium 70 and the test object 80. Part of the test light passes through the medium 70 and the glass prism 130. The remaining light of the test light passes only through the medium 70. Each light transmitted through the container 60 interferes with the reference light in the beam splitter 26 to form interference light, and is detected by the detector 92 (for example, CCD or CMOS sensor) through the imaging lens 121. The interference signal detected by the detector 92 is sent to the computer 100.

  The detector 92 is arranged at a conjugate position with the position of the test object 80 and the glass prism 130. If the phase refractive index of the test object 80 and the medium 70 is different, the light transmitted through the test object 80 becomes divergent light or convergent light. When the divergent light (converged light) intersects with light transmitted through other than the test object 80, an aperture or the like may be arranged behind the test object 80 (detector 92 side) to cut stray light. The glass prism preferably has a phase refractive index approximately equal to the phase refractive index of the medium 70 so that the interference fringes between the light transmitted through the glass prism 130 and the reference light do not become too dense. The optical path lengths of the test light and the reference light are adjusted to be equal in a state where the test object 80 and the glass prism 130 are not arranged on the test light path.

  The procedure for calculating the phase refractive index of the test object 80 of the present embodiment is as follows. In the present embodiment, the gradient relating to the wavelength of the phase difference is used as the physical quantity.

  First, the phase refractive index of the reference specimen is acquired (acquisition step S10). The phase difference between the test light transmitted through the test object and the reference light and the refractive index of the medium 70 are measured by the wavelength scanning by the spectroscope 95 and the phase shift method using the drive mechanism of the mirror 31.

The gradient dφ ₁ (λ) / dλ relating to the wavelength of the phase difference, which is the first physical quantity, is calculated (first calculation step S20). The phase refractive index of the test object 80 is calculated using the first physical quantity and the phase refractive index of the reference test object (second calculation step S30). A second physical quantity dφ ₂ (λ) / dλ, which is a function of the phase refractive index calculated in the second calculation step, is calculated (third calculation step S40), and the first physical quantity and the second physical quantity are compared. (S50). The relationship between the group refractive index and the phase refractive index of the reference test object is changed so that the first physical quantity and the second physical quantity become small (S60), and the phase refractive index is recalculated (recalculation step).

  It is also possible to feed back the results measured using the apparatus and method described in Examples 1 to 3 to a method for manufacturing an optical element such as a lens.

  FIG. 7 shows an example of a manufacturing process of an optical element using molding.

  The optical element is manufactured through an optical element design process, a mold design process, and an optical element molding process using the mold. The molded optical element is evaluated for its shape accuracy, and when the accuracy is insufficient, the mold is corrected and molded again. If the shape accuracy is good, the optical performance of the optical element is evaluated. By incorporating the refractive index measurement method of the present invention into this optical performance evaluation step, it is possible to accurately mass-produce molded optical elements.

  If the optical performance is low, the optical element whose optical surface is corrected is redesigned.

  Each embodiment described above is only a representative example, and various modifications and changes can be made to each embodiment in carrying out the present invention.

DESCRIPTION OF SYMBOLS 10 Light source 60 Container 70 Medium 80 Test object 90 Detector 100 Computer

Claims (17)

An interference signal obtained by dividing light from a light source into test light and reference light, causing the test light to enter the test object, and causing the test light transmitted through the test object and the reference light to interfere with each other. A refractive index measurement method for measuring a phase refractive index of the test object using:
An acquisition step of acquiring a phase refractive index of the reference specimen;
A first calculation step of calculating a first physical quantity that is a function of a phase refractive index of the test object using the interference signal;
A second calculating step of calculating the phase refractive index of the test object using the first physical quantity and the phase refractive index of the reference test object;
A third calculation step of calculating a second physical quantity that is a function of the phase refractive index of the test object calculated in the second calculation step;
Changing the phase refractive index of the reference specimen so that the difference between the first physical quantity and the second physical quantity is small, and using the changed phase refractive index of the reference specimen, the specimen A recalculation step of recalculating the phase refractive index of
A refractive index measurement method characterized by comprising:   The refractive index measurement method according to claim 1, wherein the first physical quantity and the second physical quantity are a phase difference between the test light and the reference light.   2. The refractive index measurement method according to claim 1, wherein the first physical quantity and the second physical quantity are inclinations with respect to a wavelength of a phase difference between the test light and the reference light.   The refractive index measurement method according to claim 1, wherein the first physical quantity and the second physical quantity are a group refractive index of the test object.   2. The phase refractive index of the test object is measured using an interference signal obtained in a state where the test object is disposed in a medium having a phase refractive index higher than that of air. 5. The refractive index measurement method according to any one of items 1 to 4.   Measuring the phase refractive index of the test object using an interference signal obtained by arranging the test object in a medium having a group refractive index equal to the group refractive index of the test object at a specific wavelength. The refractive index measurement method according to claim 1, wherein: In the first calculation step,
The phase difference between the test light and the reference light calculated from the interference signal obtained when the temperature of the test object is the first temperature, and the temperature of the test object is the first temperature. Using the phase difference between the test light and the reference light calculated from interference signals obtained at different second temperatures, and the temperature coefficient of the refractive index of the test object, The refractive index measurement method according to claim 1, wherein the first physical quantity from which the influence of thickness is removed is calculated. In the first calculation step,
A phase difference between the test light and the reference light calculated from an interference signal obtained when the test object is disposed in the first medium, and a refractive index of the first medium with the test object Removes the influence of the thickness of the test object by using the phase difference between the test light and the reference light calculated from the interference signal obtained in the state of being arranged in the second medium having a different refractive index. The refractive index measurement method according to claim 1, wherein the first physical quantity is calculated. Molding the optical element;
And a step of evaluating the molded optical element by measuring the refractive index of the optical element using the refractive index measurement method according to any one of claims 1 to 8. A method for manufacturing an optical element. A light source;
An interference optical system that divides light from the light source into test light and reference light, causes the test light to enter the test object, and causes the test light transmitted through the test object to interfere with the reference light; ,
Detecting means for detecting interference light between the test light and the reference light;
A refractive index measurement device comprising a calculation means for calculating a phase refractive index of the test object using an interference signal output from the detection means,
The calculation means obtains a phase refractive index of a reference specimen, calculates a first physical quantity that is a function of the phase refractive index of the specimen using the interference signal, and calculates the first physical quantity and the A phase refractive index of the test object is calculated using a phase refractive index of a reference test object, a second physical quantity that is a function of the calculated phase refractive index of the test object is calculated, and the first The phase refractive index of the reference specimen is changed so that the difference between the physical quantity and the second physical quantity is small, and the phase refractive index of the specimen is changed using the changed phase refractive index of the reference specimen. The refractive index measuring device characterized by recalculating   The refractive index measurement apparatus according to claim 10, wherein the first physical quantity and the second physical quantity are a phase difference between the test light and the reference light.   The refractive index measurement apparatus according to claim 10, wherein the first physical quantity and the second physical quantity are inclinations with respect to a wavelength of a phase difference between the test light and the reference light.   The refractive index measuring apparatus according to claim 10, wherein the first physical quantity and the second physical quantity are a group refractive index of the test object. A container for accommodating the test object and a medium having a phase refractive index higher than that of air;
11. The phase refractive index of the test object is measured using an interference signal obtained in a state where the test object is disposed in a medium having a phase refractive index higher than that of air. 14. The refractive index measuring device according to any one of items 1 to 13. A container for accommodating the test object and a medium having a phase refractive index higher than that of air;
Measuring the phase refractive index of the test object using an interference signal obtained by arranging the test object in a medium having a group refractive index equal to the group refractive index of the test object at a specific wavelength. The refractive index measuring device according to claim 10.   The calculating means is configured to determine a phase difference between the test light and the reference light calculated from an interference signal obtained when the temperature of the test object is a first temperature, and the temperature of the test object is the first temperature. Using the phase difference between the test light and the reference light calculated from the interference signal obtained when the second temperature is different from the temperature of 1, and the temperature coefficient of the refractive index of the test object, The refractive index measuring apparatus according to claim 10, wherein the first physical quantity from which the influence of the thickness of the test object is removed is calculated. A container for accommodating the test object and a medium having a phase refractive index higher than that of air;
The calculation means includes a phase difference between the test light and the reference light calculated from an interference signal obtained in a state in which the test object is disposed in the first medium, and the test object is the first test object. Using the phase difference between the test light and the reference light calculated from the interference signal obtained in the state of being arranged in the second medium having a refractive index different from the refractive index of the medium, the test object The refractive index measurement apparatus according to claim 10, wherein the first physical quantity from which the influence of thickness is removed is calculated.

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