CN109406106B - Method for evaluating uniformity of refractive index of optical material - Google Patents
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- CN109406106B CN109406106B CN201811218909.9A CN201811218909A CN109406106B CN 109406106 B CN109406106 B CN 109406106B CN 201811218909 A CN201811218909 A CN 201811218909A CN 109406106 B CN109406106 B CN 109406106B
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Abstract
The invention relates to an evaluation method of optical material refractive index uniformity, and relates to the technical field of optical material refractive index uniformity evaluation. The invention establishes close relation between the defect of the uniformity of the refractive index of the optical material and the use influence thereof, provides a new evaluation concept, index and uncertainty relation of the uniformity of the refractive index of the optical material, establishes a mathematical calculation method of the evaluation relation, and designs a new evaluation method of the uniformity of the refractive index of the optical material based on the proposed mathematical calculation method. The method for evaluating the uniformity of the refractive index of the optical material can reflect the influence of the uniformity of the refractive index on the imaging of an optical system when the optical material is used, can reflect the influence of an optical material process technology on the uniformity of the refractive index of the optical material, can provide reasonable evaluation indexes and methods for the uniformity test of the optical material, and can also provide more reliable index of the uniformity of the refractive index for the design of an optical system with high imaging quality.
Description
Technical Field
The invention relates to the technical field of evaluation of the uniformity of the refractive index of an optical material, in particular to an evaluation method of the uniformity of the refractive index of the optical material.
Background
The problem of the uniformity of the refractive index of the optical material is a defect of the non-uniformity of the refractive index of the optical material caused by the problem of the optical material refining process, and the defect can seriously affect the imaging quality of an optical system, so that an evaluation method is needed for evaluating the problem degree of the uniformity of the refractive index of the optical material so as to effectively control the defect of the uniformity of the refractive index of the optical material and guarantee the quality of the optical material. The prior method for evaluating the uniformity of the refractive index of an optical material uses the index delta n of the maximum variation of the refractive index in the optical materialPVTo evaluate the homogeneity of the optical material, i.e. to use the maximum refractive index n in the optical materialmaxReducing the minimum refractive index nminA difference of (1), i.e. Δ nPV＝mmax-mmin，ΔnPVCommonly referred to as the peak to valley refractive index of the optical material.
It can be seen that the prior method for evaluating the uniformity of the refractive index of the optical material adoptsIndex of maximum variation of refractive index, i.e. peak-to-valley value of refractive index Δ nPVThis value reflects only a local extreme problem of the refractive index uniformity of the optical material, and does not reflect the refractive index uniformity problem over the entire use face of the optical material, and thus does not reliably reflect the actual effect of the refractive index uniformity problem of the optical material on the imaging quality of the optical system. Peak to valley refractive index Δ nPVIs more suitable for expressing the uniformity of the material refining process. Heretofore, the index for testing the uniformity of the refractive index of an optical material and the index for controlling the uniformity of the optical material in an optical system have been usedPVThis index will give results from optical material uniformity tests that do not reliably evaluate the refractive index uniformity problem of the material, and also provide unreliable basis for refractive index uniformity for optical system image quality design. For example: the optical material in FIG. 1 has a large refractive index difference peak-to-valley value Δ n on the micro-surface element of the used area (light transmission area)PVAnd the whole material has small refractive index difference peak-to-valley value delta nPV(ii) a The micro-surface element with the used area (light transmission area) of the optical material in FIG. 2 has smaller peak-to-valley value of refractive index difference DeltanPVAnd the whole material has a small refractive index difference peak-to-valley value delta nPV. Because the imaging quality of the optical system is determined by the integrity of the light-transmitting area of the optical system, the problem of uniformity of the material occupying a small area of the light-transmitting area of the whole aperture (even if serious) will not affect the imaging quality of the optical system, and the problem of uniformity of the material occupying a large area of the light-transmitting area of the whole aperture will significantly affect the imaging quality of the optical system. In practice, although the local maximum refractive index difference peak-to-valley value Δ n in fig. 1PVSignificantly larger than the local maximum refractive index difference peak-to-valley value Δ n in fig. 2PVHowever, the optical material uniformity problem of fig. 2 has a significantly greater effect on the imaging quality of the optical system than that of fig. 1. Whereas the problem of fig. 1 is greater than that of fig. 2 according to the prior evaluation method of the uniformity of the refractive index of the optical material, which causes a problem phenomenon that the prior evaluation method is unreliable and not in practical use. Due to the peak-to-valley value of the refractive index Δ n of the optical materialPVIs obtained by simple calculationIn addition, the quantity of test information of the algorithm applied material problem is not enough and the mathematical calculation processing relation is not much, so that the problem of the uniformity of the refractive index of the optical material is difficult to comprehensively and really express.
Disclosure of Invention
Technical problem to be solved
The technical problem to be solved by the invention is as follows: how to design a new method for evaluating the uniformity of the optical material to ensure that the evaluation of the refraction uniformity of the optical material meets the requirements of comprehensiveness and accuracy of actual evaluation.
(II) technical scheme
In order to solve the technical problem, the invention provides an evaluation method of the refractive index uniformity of an optical material, which comprises the following steps:
s1 refractive index value n for ith point or bin of test surface of optical material sample tested by interference test method or other test methodi(x, y) are counted, the number of the statistics is N points or surface elements, and the nominal refractive index value of the optical material sample is N0Calculating the variation Deltan of the ith point or bin relative to the nominal refractive index of the optical material samplei(x,y)；
S2, calculating the average value of N points of the variation of the refractive index of the ith test point of the optical material sample according to the calculation result of the step S1
S3, calculating the standard deviation value delta n of the refractive index variation of the optical material test point according to the calculation result of the step S2STD；
S4, determining the peak-to-valley value delta n of the refractive index of the optical material test pointPV：
S5, establishing the average value of the standard deviation value of the optical material refractive index uniformity
Calculating the standard deviation value delta n of the jth testSTDjAverage of M tests
S6, establishing the average value of the peak value and the valley value of the uniformity of the refractive index of the optical material
The refractive index uniformity peak-to-valley value delta n of the jth test is calculatedPVjAverage of M tests
S7, average value
Calculating the average value of the standard deviation of the refractive index uniformity
Uncertainty u ofSTD；
S8, average value
Calculating the average value of the peak-to-valley values of the refractive index uniformity
Uncertainty u ofPV；
S9, use
And
as an index for evaluating the uniformity of refractive index of an optical material, use is made of
Evaluation of uniformity of refractive index of the entire surface of the optical material
As surfaces for optical materialsIndex for evaluating extreme difference in refractive index uniformity
And
evaluating the uniformity of the refractive index of the optical material by two indexes;
s10, according to the uncertainty uSTDAnd uncertainty of uPVAnd determining the uncertainty influence magnitude range of the evaluation value of the uniformity of the refractive index of the optical material.
Preferably, in step S1, the variation Δ n of the ith point or bin with respect to the nominal refractive index of the optical material sample is calculated according to equation (1)i(x,y)：
Δni(x,y)＝ni(x,y)-n0(1)。
Preferably, in step S2, the average value of the change amount of the refractive index of the test surface of the optical material sample is calculated according to the formula (2)
Preferably, in step S3, the standard deviation Δ n of the refractive index variation of the test surface of the optical material is calculated according to equation (3)STD：
Preferably, in step S5, the standard deviation mean value
Calculating according to the formula (5):
preferably, step S6In the above, the refractive index uniformity peak-to-valley value Deltan of the jth test was calculated according to the formula (6)PViM times (M)>Average value of 3) test
Preferably, in step S7, the average value of the standard deviation of refractive index uniformity is calculated according to equation (7)
Uncertainty u ofSTD：
Average value of standard deviation of refractive index uniformity when number of test M of specimen increases
Uncertainty u ofSTDDecreasing, the number of start segments being such that uSTDThe rate of decrease is faster, the latter times being uSTDThe rate of decrease slows down.
Preferably, in step S8, the average value of the peak-to-valley values of the uniformity of refractive index is calculated according to equation (8)
Uncertainty u ofPV：
Average value of peak-to-valley values of refractive index uniformity when number of test times M of specimen was increased
Uncertainty u ofPVDecreasing, the number of start segments being such that uPVThe rate of decrease is smallerFast, the latter times making uPVThe rate of decrease slows down.
Preferably, M > -3.
(III) advantageous effects
The invention establishes close relation between the defect of the uniformity of the refractive index of the optical material and the use influence thereof, provides a new evaluation concept, index and uncertainty relation of the uniformity of the refractive index of the optical material, establishes a mathematical calculation method of the evaluation relation, and designs a new evaluation method of the uniformity of the refractive index of the optical material based on the proposed mathematical calculation method. The method for evaluating the uniformity of the refractive index of the optical material can reflect the influence of the uniformity of the refractive index on the imaging of an optical system when the optical material is used, can reflect the influence of an optical material process technology on the uniformity of the refractive index of the optical material, can provide reasonable evaluation indexes and methods for the uniformity test of the optical material, and can also provide more reliable index of the uniformity of the refractive index for the design of an optical system with high imaging quality. The uncertainty algorithm given in the method for evaluating the uniformity of the refractive index of the optical material can also provide the uncertainty influence quantity range of the evaluation value of the uniformity of the refractive index of the optical material, so that the high-precision design requirement can be better ensured. The method for evaluating the uniformity of the refractive index of the optical material has wide applicability, and can be used for evaluating the uniformity of the refractive index of visible light optical materials, infrared optical materials, ultraviolet optical materials and the like.
Drawings
FIG. 1 is a graph of the distribution of local prominent variations in the uniformity of the refractive index of a sample;
FIG. 2 is a distribution pattern diagram showing the overall significant variation in the uniformity of the refractive index of a sample;
fig. 3 is a statistical relationship diagram of the distribution of refractive index uniformity test values.
Detailed Description
In order to make the objects, contents and advantages of the present invention clearer, the following detailed description of the embodiments of the present invention will be made in conjunction with the accompanying drawings and examples.
The inventors of the present invention have found that the distribution points of the used surface of the optical material are distributedOr the refractive index of the surface element is counted, and the variation quantity delta n of each point relative to the nominal value of the refractive index is calculatedi(x, y) calculating a standard deviation value [ Delta ] n of the refractive index change amount at each pointSTDThen, the average value of the refractive index variation standard deviation value of a plurality of tests is calculated
The evaluation value is used as the evaluation value of the refractive index uniformity of the optical material, the practical influence of the problem of the refractive index uniformity of the whole surface of the optical material on the imaging quality of an optical system can be comprehensively reflected, and the peak value and the valley value delta n of the refractive index uniformity are givenPVIs matched to establish the main index of the refractive index uniformity evaluation
And auxiliary index
The uncertainty algorithm can establish a perfect evaluation relation which can completely and truly reflect and extremely reflect the uniformity of the optical material.
According to the above invention, the method for evaluating the uniformity of the refractive index of the optical material mainly comprises the following steps of establishing an evaluation value concept, an index, a mathematical algorithm and an uncertainty algorithm of the uniformity of the refractive index of the optical material:
s1, refractive index value n of ith point or bin of optical material sample test surface (or use surface) tested by interference test method or other test methodi(x, y) are counted, the number of the statistics is N points or bins, as shown in FIG. 3, and the nominal refractive index value of the optical material sample is N0The variation Deltan of the ith point or bin with respect to the nominal refractive index of the optical material sample is calculated according to equation (1)i(x,y)。
Δni(x,y)＝ni(x,y)-n0(1)
S2, calculating the average value of the variation of the refractive index of the test surface (or the use surface) of the optical material sample according to the formula (2)
S3, calculating the standard deviation value delta n of the refractive index variation of the optical material test point according to the following formula (3)STD。
S4, calculating the peak-to-valley value delta n of the refractive index of the optical material test point according to the following formula (4)PV。
ΔnPV＝nmax-nmin(4)
S5, standard deviation value delta n of refractive index variation due to one testSTDIs theoretically infinite, and therefore, the standard deviation value of the refractive index change Δ n of one test isSTDAnd cannot be used as an evaluation index. In order to obtain reliable evaluation of the refractive index uniformity of the optical material, the standard deviation value deltan of the jth test needs to be obtained through multiple testsSTDjM times (M)>Average value of 3) test
Using the standard deviation value delta n of the refractive index variation of the optical materialSTDAverage value of (2)
As a main index for evaluation of uniformity of refractive index, standard deviation average
Calculated as the following formula (5).
S6, establishing the average value of the peak-to-valley values of the refractive index uniformity of the optical material according to the thought and the algorithm of S5
The refractive index uniformity peak-to-valley value Deltan of the jth test is calculated according to the following formula (6)PVjM times (M)>Average value of 3) test
Peak-to-valley value Deltan of refractive index variation of optical materialPVAverage value of (2)
As a secondary index for the evaluation of refractive index uniformity.
S7, calculating the average value of the standard deviation of the refractive index uniformity according to the following formula (7)
Uncertainty u ofSTD。
Average value of standard deviation of refractive index uniformity when number of test M of specimen increases
Uncertainty u ofSTDWill be reduced, the number of start segments will be such that uSTDThe rate of decrease is faster, the latter times being uSTDThe rate of decrease slows down.
S8, calculating the average value of the peak-to-valley values of the uniformity of the refractive index according to the following formula (8)
Uncertainty u ofPV。
Similarly, as the number of test times M of the sample increases, the average value of the peak-to-valley values of the uniformity of the refractive index
Uncertainty u ofPVWill be reduced, the number of start segments will be such that uPVThe rate of decrease is faster, the latter times being uPVThe rate of decrease slows down.
S9, use
And
as an index for evaluating the uniformity of refractive index of an optical material, use is made of
Evaluation of uniformity of refractive index of the entire surface of the optical material
As an index for evaluating an extreme difference in refractive index uniformity of a surface using an optical material
And
evaluating the uniformity of the refractive index of the optical material by two indexes;
s10, according to the uncertainty uSTDAnd uncertainty of uPVAnd determining the uncertainty influence magnitude range of the evaluation value of the uniformity of the refractive index of the optical material.
It can be seen that the invention designs an evaluation method for the refractive index uniformity of an optical material, which uses an index capable of reflecting the refractive index uniformity of the whole using surface of the optical material and an index of extreme difference of the refractive index uniformity to evaluate the refractive index uniformity of the optical material (i.e. an evaluation method for two indexes), wherein one index is a main evaluation index, and the other index is a main evaluation indexThe individual indexes are auxiliary evaluation indexes. The main evaluation index is the core content, is used for reflecting the integral problem of the refractive index uniformity of the using surface of the optical material, and uses the refractive index uniformity standard difference value delta nSTDIs expressed as a mean value of; auxiliary evaluation index Using peak-to-valley value Deltan of surface refractive index uniformity in use of optical MaterialPVIs expressed as a mean value of; in order to master and control the test and design precision of two evaluation indexes, a refractive index uniformity standard difference value delta n is establishedSTDAverage value of (2)
And peak-to-valley value of refractive index uniformity Δ nPVAverage value of (2)
An uncertainty algorithm of (1). The new method for evaluating the uniformity of the optical material can reflect the actual influence of the uniformity problem of the optical material on the imaging quality of an optical system and can also reflect the extreme value degree of nonuniformity caused by the material process, so that the evaluation of the refraction uniformity of the optical material meets the requirements of comprehensiveness and accuracy of actual evaluation.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.
Claims (8)
1. The method for evaluating the uniformity of the refractive index of the optical material is characterized by comprising the following steps of:
s1 refractive index value n for ith point or bin of test surface of optical material sample tested by interference test method or other test methodi(x, y) are counted, the number of the statistics is N points or surface elements, and the nominal refractive index value of the optical material sample is N0Calculating the variation Deltan of the ith point or bin relative to the nominal refractive index of the optical material samplei(x,y)；
S2, calculating the refractive index of the ith test point of the optical material sample according to the calculation result of the step S1Change amount of (a) niAverage value of N points of (x, y)
S3, calculating the standard deviation value delta n of the refractive index variation of the optical material test point according to the calculation result of the step S2STD；
S4, determining the peak-to-valley value delta n of the refractive index of the optical material test pointPV：
S5, establishing the average value of the standard deviation value of the optical material refractive index uniformity
Calculating the standard deviation value delta n of the jth testSTDjAverage of M tests
S6, establishing the average value of the peak value and the valley value of the uniformity of the refractive index of the optical material
The refractive index uniformity peak-to-valley value delta n of the jth test is calculatedPVjAverage of M tests
S7, average value
Calculating the average value of the standard deviation of the refractive index uniformity
Uncertainty u ofSTD；
S8, average value
Calculating the average value of the peak-to-valley values of the refractive index uniformity
Uncertainty u ofPV；
S9, use
And
as an index for evaluating the uniformity of refractive index of an optical material, use is made of
Evaluation of uniformity of refractive index of the entire surface of the optical material
As an index for evaluating an extreme difference in refractive index uniformity of a surface using an optical material
And
evaluating the uniformity of the refractive index of the optical material by two indexes;
s10, according to the uncertainty uSTDAnd uncertainty of uPVAnd determining the uncertainty influence magnitude range of the evaluation value of the uniformity of the refractive index of the optical material.
2. The method of claim 1, wherein in step S1, the variation Δ n of the ith point or bin with respect to the nominal refractive index of the optical material sample is calculated according to equation (1)i(x,y)：
Δni(x,y)＝ni(x,y)-n0(1)。
3. Such as rightThe method according to claim 2, wherein in step S2, the average value of the change amounts of the refractive index of the test surface of the optical material sample is calculated according to equation (2)
4. The method of claim 3, wherein in step S3, the standard deviation value Δ n of the refractive index variation of the test surface of the optical material is calculated according to equation (3)STD：
5. The method of claim 4, wherein in step S5, the mean of the standard deviation
Calculating according to the formula (5):
6. the method of claim 5, wherein in step S6, the refractive index uniformity peak-to-valley value Δ n of the jth test is calculated according to equation (6)PViM times (M)>Average value of 3) test
7. The method of claim 6, wherein in step S7, the average value of the standard deviation values of refractive index uniformity is calculated according to equation (7)
Uncertainty u ofSTD：
Average value of standard deviation of refractive index uniformity when number of test M of specimen increases
Uncertainty u ofSTDDecreasing, the number of start segments being such that uSTDThe rate of decrease is faster, the latter times being uSTDThe rate of decrease slows down.
8. The method of claim 7, wherein in step S8, the average value of the peak-to-valley values of the uniformity of the refractive index is calculated according to equation (8)
Uncertainty u ofPV：
Average value of peak-to-valley values of refractive index uniformity when number of test times M of specimen was increased
Uncertainty u ofPVDecreasing, the number of start segments being such that uPVThe rate of decrease is faster, the latter times being uPVThe rate of decrease slows down.
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| US7245361B2 (en) * | 2002-06-04 | 2007-07-17 | Nikon Corporation | Method for evaluating refractive index homogeneity of optical member |
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