A device and method for detecting uniformity of a narrow-band filter spectral space

By combining an integrating sphere light source and a telecentric objective lens with a frame-shifting CCD detector, the problem of low detection efficiency for spectral spatial inhomogeneity of narrowband filters is solved, achieving high-precision and low-cost batch detection.

CN116735166BActive Publication Date: 2025-12-19HEFEI INSTITUTE OF PHYSICAL SCIENCE CHINESE ACADEMY OF SCIENCES
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Patent Information

Application Number
CN202310829884.0
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2023-07-07
Publication Date
2025-12-19
Estimated Expiration
2043-07-07

AI Technical Summary

Technical Problem

In existing technologies, the detection efficiency of spectral spatial inhomogeneity of narrowband filters is low and the cost is high, making it difficult to apply to the spectral spatial detection of a large number of filters.

Method used

A combination of an integrating sphere light source, a reference narrowband filter, an object-side field-of-view aperture, an object-side telecentric objective lens, a sample of the narrowband filter under test, a mounting assembly for the narrowband filter under test, an area array CCD detector, and a data acquisition system is used to achieve high-precision and rapid detection through an object-side telecentric optical path and a frame-shifting CCD detector.

Benefits of technology

It enables high-precision, batch-scale, and rapid detection of narrowband filter spectral space, reducing manpower and time costs and improving detection efficiency and accuracy.

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Abstract

The present application provides a kind of narrow-band filter spectral space uniformity detection device and method, the device includes integrating sphere, reference band-pass filter, object field diaphragm, object telecentric objective, area array CCD detector, narrow-band filter sample installation component, data acquisition system, wherein, object telecentric objective includes front lens barrel component and rear lens barrel component;Narrow-band filter sample installation component is placed in the object telecentric light path of front lens barrel component, and CCD detector is located in the focal plane of object telecentric lens.The present application obtains the uniformity of the spectral space of narrow-band filter by comparing the spectral response values obtained by data acquisition system in the case of having narrow-band filter sample and the case of not having narrow-band filter sample.The device structure of the present application is simple, does not need motion mechanism, and can obtain the spectral space uniformity of narrow-band filter in single detection, with high detection efficiency, saves time and labor cost, and is especially suitable for batch measurement.
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Description

TECHNICAL FIELD

[0001] The present application relates to the field of optical detection, in particular to a narrow-band filter spectral space uniformity detection device and method. BACKGROUND

[0002] In a multi-spectral polarization detection instrument, a narrow-band filter is generally used to realize multi-spectral detection. In order to ensure the polarization detection accuracy of the instrument, a narrow-band filter with high spectral performance space uniformity needs to be used. The spectral space non-uniformity of the narrow-band filter mainly includes: internal stress non-uniformity caused by the processing process, leading to optical transmittance non-uniformity; spectral shape, bandwidth, center wavelength and other optical performance space non-uniformity caused by the process in the coating process. Therefore, before the filter is installed in the whole machine, it is necessary to detect the spectral space uniformity of the narrow-band filter, and select the narrow-band filter with spectral space uniformity. The traditional method generally uses a spectrophotometer to detect in different regions, but this method has very high labor and time cost, and the data processing process is complicated, which is difficult to apply to the spectral space uniformity detection of filters with multiple quantities and specifications. SUMMARY

[0003] The present application is to solve the above-mentioned deficiencies in the prior art, and provides a narrow-band filter spectral space uniformity detection device and method, in order to realize high-precision and batch rapid detection of the spectral space uniformity of the narrow-band filter, so as to improve the detection efficiency and accuracy.

[0004] In order to achieve the above-mentioned application purposes, the present application adopts the following technical solutions:

[0005] The narrow-band filter spectral space uniformity detection device of the present application comprises, in sequence: an integrating sphere light source, a reference narrow-band filter, an object field stop, an object telecentric objective lens, a narrow-band filter sample to be detected, a narrow-band filter mounting assembly, a surface array CCD detector and a data acquisition system.

[0006] The integrating sphere light source is used to uniformly illuminate the object field stop, and the object field stop is installed at the front end of the object telecentric objective lens.

[0007] The object telecentric objective lens comprises, in sequence from the object side to the image side: a front lens barrel, a first compression ring, a first lens, a first spacer ring, a second lens, a second compression ring, a third lens, a fourth lens, an aperture stop, a rear lens barrel, a fifth lens, a sixth lens, a third compression ring, a seventh lens, an eighth lens, a second spacer ring, and a ninth lens.

[0008] The first lens is a double convex lens, the second lens is a convex positive meniscus lens, the third lens is a double convex lens, the fourth lens is a double concave lens, the fifth lens is a flat concave lens, the sixth lens is a flat convex lens, the seventh lens is a double convex lens, the eighth lens is a convex negative meniscus lens, and the ninth lens is a double convex lens;

[0009] The third lens and the fourth lens are combined as a double cemented lens, the fifth lens and the sixth lens are combined as a double cemented lens, and the seventh lens and the eighth lens are combined as a double cemented lens.

[0010] The front lens barrel, the first pressing ring, the first lens, the first spacer ring, the second lens, the second pressing ring, the third lens and the fourth lens constitute a front lens barrel assembly.

[0011] The rear lens barrel, the fifth lens, the sixth lens, the third pressing ring, the seventh lens, the eighth lens, the second spacer ring, the ninth lens and the fourth pressing ring constitute a rear lens barrel assembly.

[0012] The aperture stop is located between the fourth lens and the fifth lens.

[0013] The narrow-band filter mounting assembly to be detected is mounted at the front end position of the first lens and is located in the object side telecentric light path of the object side telecentric objective lens.

[0014] The face array CCD detector is mounted at the rear end of the rear lens barrel assembly, and is focused and positionally fixed through the thread on the object side telecentric objective lens and the locking nut.

[0015] The face array CCD detector is located on the focal plane of the object side telecentric objective lens.

[0016] The light beam emitted by the integrating sphere light source is transmitted through the reference narrow-band filter, so that the effective light rays in the spectral bandwidth are transmitted, a light spot is formed on the object side field stop, the light spot is incident into the object side telecentric objective lens, and is irradiated to the narrow-band filter sample to be detected in the front lens barrel assembly in a region, then a collimated light beam is formed after passing through the first lens, the second lens, the third lens and the fourth lens, the collimated light beam is focused again through the rear lens barrel assembly, and an image is formed on the face array CCD detector, and the image is collected by the data acquisition system.

[0017] The narrow-band filter spectral space uniformity detection device has the characteristics that the center wavelength of the reference narrow-band filter is the same as that of the narrow-band filter sample to be detected, and the bandwidth of the reference narrow-band filter is not less than that of the narrow-band filter sample to be detected.

[0018] The area array CCD detector adopts a frame transfer type CCD detector.

[0019] The integrating sphere light source adopts a halogen lamp as an illumination light source.

[0020] The magnification of the object side telecentric objective lens is between 0.3 and 1.5.

[0021] The narrow-band filter spectral space uniformity detection method has the characteristics that it is applied to the uniformity detection device, and comprises the following steps:

[0022] Step 1, the data acquisition system performs multiple image acquisition on the imaging on the area array CCD detector, obtains a plurality of spectral response values, and then performs image averaging, background subtraction and frame transfer correction preprocessing on all the spectral response values, to obtain the image gray value of the full image plane {DN1(i,j)|i,j=1,2,…,N}, wherein DN1(i,j) represents the gray value of the i-th row and j-th column pixel; and N represents the number of pixels.

[0023] Step 2, the narrow-band filter sample to be detected is taken out from the narrow-band filter mounting assembly, and the axial distance between the area array CCD detector and the vertex of the image side of the ninth lens is adjusted, so that clear imaging can be formed on the area array CCD detector.

[0024] Step 3, the data acquisition system is used to perform multiple image acquisition on the imaging on the area array CCD detector, to obtain a plurality of spectral response values without the sample; and then image averaging, background subtraction and frame transfer correction preprocessing are performed on all the spectral response values without the sample, to obtain the image gray value of the full image plane without the sample {DN2(i,j)|i,j=1,2,…,N}, wherein DN2(i,j) represents the gray value of the i-th row and j-th column pixel without the sample.

[0025] Step 4, the i-th row and j-th column surface uniformity of the narrow-band filter sample to be detected is calculated. Thus, the surface uniformity of the narrow-band filter sample to be detected is obtained.

[0026] Compared with the prior art, the present application has the following beneficial effects:

[0027] 1, the present application places the filter to be detected in the object side telecentric optical path, and according to the illumination form of the filter in different regions, the difference between the pixels of the detector is the uniformity of the spectral space of the filter, so that the uniformity test can be completed by single measurement, and the problem of low efficiency caused by the need for multiple regional measurements in the traditional spectrophotometer method is solved.

[0028] 2、The application can realize quick installation and dismounting of the filter to be tested by using the plug-in structure, without complex movement structure, with low precision requirement for filter installation, simple structure, low stray light influence, simple and feasible data processing method, high measurement precision, and being particularly suitable for high-precision uniformity detection of spectral space of filters with multiple quantity and specifications.

[0029] 3、The application adopts an object far field objective lens, all lenses are spherical lenses, with loose precision requirement for machining and adjustment, high engineering feasibility and strong reliability. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 is a schematic diagram of a narrow-band filter spectral uniformity detection device of the application;

[0031] Figure 2 is a schematic diagram of an optical path structure of an object far field objective lens of the application;

[0032] Figure 3 is a uniformity test result diagram of a narrow-band filter spectral space in an embodiment of the application;

[0033] The reference narrow-band filter is 2, the object field stop is 3, the object far field objective lens is 4, the narrow-band filter is 5, the narrow-band filter mounting assembly is 6, the area array CCD detector is 7, the data acquisition system is 8, the front lens barrel assembly is 9, the rear lens barrel assembly is 10, the first lens is L1, the second lens is L2, the third lens is L3, the fourth lens is L4, the aperture stop is L5, the fifth lens is L6, the sixth lens is L7, the seventh lens is L8, the eighth lens is L9, the ninth lens is L10, the front lens barrel is C1, the first pressing ring is M1, the first spacer ring is M2, the second pressing ring is M3, the rear lens barrel is C2, the third pressing ring is M4, the second spacer ring is M5, and the fourth pressing ring is M6. DETAILED DESCRIPTION

[0034] For example, the uniformity of the spectral space of a narrow-band filter applied to a certain type of task is tested, the filter has a center wavelength of 670 nm, a bandwidth of 20 nm, a center thickness of 4 mm, an effective aperture of 40 mm, and an average spectral transmittance of greater than 95%. According to the drawings, in this embodiment, a narrow-band filter spectral space uniformity detection device is as shown in Figure 1As shown, sequentially includes: integrating sphere light source 1, reference narrowband filter 2, object field stop 3, object telecentric objective 4, to be measured narrowband filter sample 5, to be measured narrowband filter mounting assembly 6, area array CCD detector 7 and data acquisition system 8;Integrating sphere light source 1 adopts the integrating sphere with the aperture of 50mm produced by Labsphere company, and the illumination light source is halogen lamp, which is used for uniform illumination object field stop 3, and the object field stop 3 is installed at the front end of object telecentric objective 4, and the aperture of the stop is 30mm.

[0035] In the embodiment, as shown in the figure, Figure 2 Object telecentric objective 4 sequentially includes: front lens barrel C1, first pressing ring M1, first lens L1, first spacer ring M2, second lens L2, second pressing ring M3, third lens L3, fourth lens L4, aperture stop L5, rear lens barrel C2, fifth lens L6, sixth lens L7, third pressing ring M4, seventh lens L8, eighth lens L9, second spacer ring M5, ninth lens L10 arranged from object side to image side.

[0036] Among them, the first lens L1 is a biconvex lens, the second lens L2 is a convex object side positive crescent lens, the third lens L3 is a biconvex lens, the fourth lens L4 is a double concave lens, the fifth lens L6 is a flat concave lens, the sixth lens L7 is a flat convex lens, the seventh lens L8 is a biconvex lens, the eighth lens L9 is a convex image side negative crescent lens, and the ninth lens L10 is a biconvex lens.

[0037] Among them, the third lens L3 and the fourth lens L4 are combined into a double cemented lens, the fifth lens L6 and the sixth lens L7 are combined into a double cemented lens, and the seventh lens L8 and the eighth lens L9 are combined into a double cemented lens.

[0038] Among them, the front lens barrel C1, the first pressing ring M1, the first lens L1, the first spacer ring M2, the second lens L2, the second pressing ring M3, the third lens L3 and the fourth lens L4 constitute the front lens barrel assembly 9, and the rear lens barrel C2, the fifth lens L6, the sixth lens L7, the third pressing ring M4, the seventh lens L8, the eighth lens L9, the second spacer ring M5 and the ninth lens L10 constitute the rear lens barrel assembly 10.

[0039] The aperture stop L5 is located between the fourth lens L4 and the fifth lens L6.

[0040] The rear end of the rear lens barrel assembly 10 is mounted with a face array CCD detector 7, and the face array CCD detector 7 is focused and positionally fixed through the screw thread and locking nut on the object side telecentric objective lens; the narrow-band filter under test installation assembly 6 is installed at the front end of the first lens L1 and is in the object side telecentric light path of the object side telecentric objective lens 4; the narrow-band filter sample 5 under test is arranged in the narrow-band filter under test installation assembly 6; the face array CCD detector 7 is a frame transfer type detector produced by E2V Company, the model of which is CCD47-20, the number of pixels of which is 1024*1024, and the face array CCD detector 7 is located at the focal plane of the object side telecentric objective lens 4.

[0041] The light beam emitted by the integrating sphere light source 1 is transmitted through the reference narrow-band filter 2, so that the effective light rays in the spectral bandwidth are transmitted, the light spot is formed on the object side field diaphragm 3, the light spot is incident into the object side telecentric objective lens 4, and the light spot is irradiated to the narrow-band filter sample under test in the front lens barrel assembly 9 in a region, then the collimated light beam is formed after passing through the first lens L1, the second lens L2, the third lens L3 and the fourth lens L4, and the collimated light beam is focused through the rear lens barrel assembly and is imaged on the face array CCD detector 7, and the image is collected by the data acquisition system 8.

[0042] The optical design data of the object side telecentric objective lens 4 in the embodiment of the application is shown in Table 1 below. The magnification of the objective lens is 0.6 times, the aperture stop L5 is located between the fourth lens L4 and the fifth lens L6, and the diameter of the aperture stop L5 is 10.5 mm.

[0043] Table 1

[0044]

[0045] In the table, the meanings of the symbols are as follows:

[0046] Stop: aperture stop L5;

[0047] R: radius of curvature of the surface of the optical lens;

[0048] R1: radius of curvature of the object side surface of the first lens L1; R2: radius of curvature of the image side surface of the first lens L1;

[0049] R3: radius of curvature of the object side surface of the second lens L2; R4: radius of curvature of the image side surface of the first lens L2;

[0050] R5: radius of curvature of the object side surface of the third lens L3; R6: radius of curvature of the image side surface of the third lens L3;

[0051] R7: radius of curvature of the image side surface of the fourth lens L4;

[0052] R8: radius of curvature of the object side surface of the fifth lens L6; R9: radius of curvature of the image side surface of the fifth lens L6;

[0053] R10: sixth lens L7 image side surface radius of curvature;

[0054] R11: seventh lens L8 object side surface radius of curvature; R12: seventh lens L8 image side surface radius of curvature;

[0055] R13: eighth lens L9 object side surface radius of curvature;

[0056] R14: ninth lens L10 object side surface radius of curvature; R15: ninth lens L10 image side surface radius of curvature;

[0057] d: center thickness of lens, on-axis distance between adjacent lenses

[0058] d1: center thickness of first lens L1; d2: on-axis distance between first lens L1 and second lens L2;

[0059] d3: center thickness of second lens L2; d4: on-axis distance between second lens L2 and third lens L3;

[0060] d5: center thickness of third lens L3; d6: center thickness of fourth lens L4;

[0061] d7: on-axis distance between fourth lens L4 and aperture stop L5;

[0062] d8: on-axis distance between aperture stop L5 and fifth lens L6; d9: center thickness of fifth lens L6;

[0063] d10: center thickness of sixth lens L7; d11: on-axis distance between sixth lens L7 and seventh lens L8;

[0064] d12: center thickness of seventh lens L8; d13: center thickness of eighth lens L9;

[0065] d14: on-axis distance between eighth lens L9 and ninth lens L10;

[0066] d15: center distance of ninth lens L10; d16: distance between ninth lens L10 and image plane;

[0067] nd: refractive index of lens; vd: Abbe number of lens;

[0068] nd1: refractive index of first lens L1, vd1: Abbe number of first lens L1;

[0069] nd2: refractive index of second lens L2, vd1: Abbe number of second lens L2;

[0070] nd3: refractive index of third lens L3, vd1: Abbe number of third lens L3;

[0071] nd4: refractive index of the fourth lens L4, vd1: Abbe number of the fourth lens L4;

[0072] nd5: refractive index of the fifth lens L5, vd1: Abbe number of the fifth lens L5;

[0073] nd6: refractive index of the sixth lens L6, vd1: Abbe number of the sixth lens L6;

[0074] nd7: refractive index of the seventh lens L7, vd1: Abbe number of the seventh lens L7;

[0075] nd8: refractive index of the eighth lens L8, vd1: Abbe number of the eighth lens L8;

[0076] nd9: refractive index of the ninth lens L9, vd1: Abbe number of the ninth lens L9;

[0077] In the embodiment, a narrow-band filter spectral space uniformity detection method is realized based on the above uniformity detection device, and the method comprises the following steps:

[0078] Step 1: The data acquisition system 8 performs multiple image acquisition on the imaging on the area array CCD detector 7 to obtain a plurality of spectral response values, and then performs image averaging, background subtraction and frame transfer correction preprocessing on all the spectral response values to obtain the image gray value of the full image plane {DN1(i,j)|i,j=1,2,…,N}, wherein DN1(i,j) represents the gray value of the i-th row and j-th column pixel; and N represents the number of pixels.

[0079] Step 2: The narrow-band filter sample 5 to be detected is taken out from the narrow-band filter mounting assembly 6, and the axial distance between the area array CCD detector 7 and the vertex of the image side of the ninth lens L10 is adjusted so that the area array CCD detector 7 can clearly image.

[0080] Step 3: The data acquisition system 8 performs multiple image acquisition on the imaging on the area array CCD detector 7 to obtain a plurality of spectral response values without the sample; and then performs image averaging, background subtraction and frame transfer correction preprocessing on all the spectral response values without the sample to obtain the image gray value of the full image plane without the sample {DN2(i,j)|i,j=1,2,…,N}, wherein DN2(i,j) represents the gray value of the i-th row and j-th column pixel without the sample.

[0081] Step 4: The surface uniformity of the i-th row and j-th column of the narrow-band filter sample 5 to be detected is calculated Thus, the surface uniformity of the narrow-band filter sample 5 to be detected is obtained {η(i,j)|i,j=1,2,…,N}.

[0082] The uniformity of the spectral space of the narrow-band filter to be tested is tested by using the above device and method, and the test result is as shown in Figure 3 The figure shows that the uniformity of the spectral space of the narrow-band filter to be tested is less than 1.2%.

Claims

1. A device for detecting uniformity of a narrow-band filter spectral space, characterized by, Comprise in sequence: The integral sphere light source (1), the reference narrowband filter (2), the object field stop (3), the object telecentric objective (4), the measured narrowband filter sample (5), the measured narrowband filter mounting assembly (6), the area array CCD detector (7) and the data acquisition system (8); The integral sphere light source (1) is used for uniform illumination of the object field stop (3); and the object field stop (3) is installed at the front end of the object telecentric objective (4); The object telecentric objective (4) comprises in sequence: front lens barrel (C1), first pressing ring (M1), first lens (L1), first spacer ring (M2), second lens (L2), second pressing ring (M3), third lens (L3), fourth lens (L4), aperture diaphragm (L5), rear lens barrel (C2), fifth lens (L6), sixth lens (L7), third pressing ring (M4), seventh lens (L8), eighth lens (L9), second spacer ring (M5), ninth lens (L10) and fourth pressing ring (M6) arranged in sequence from the object side to the image side; The first lens (L1) is a double convex lens, the second lens (L2) is a convex object side positive crescent lens, the third lens (L3) is a double convex lens, the fourth lens (L4) is a double concave lens, the fifth lens (L6) is a flat concave lens, the sixth lens (L7) is a flat convex lens, the seventh lens (L8) is a double convex lens, the eighth lens (L9) is a convex image side negative crescent lens, and the ninth lens (L10) is a double convex lens; Wherein, the third lens (L3) and the fourth lens (L4) are combined as a double cemented lens, the fifth lens (L6) and the sixth lens (L7) are combined as a double cemented lens, and the seventh lens (L8) and the eighth lens (L9) are combined as a double cemented lens; Wherein, the front lens barrel (C1), first pressing ring (M1), first lens (L1), first spacer ring (M2), second lens (L2), second pressing ring (M3), third lens (L3) and fourth lens (L4) constitute a front lens barrel assembly (9); The rear lens barrel (C2), fifth lens (L6), sixth lens (L7), third pressing ring (M4), seventh lens (L8), eighth lens (L9), second spacer ring (M5), ninth lens (L10) and fourth pressing ring (M6) constitute a rear lens barrel assembly (10); The aperture diaphragm (L5) is located between the fourth lens (L4) and the fifth lens (L6); The measured narrowband filter mounting assembly (6) is installed at the front end of the first lens (L1) and is located in the object telecentric light path of the object telecentric objective (4); the measured narrowband filter sample (5) is arranged in the measured narrowband filter mounting assembly (6); The rear end of the rear lens barrel assembly (10) is provided with the area array CCD detector (7), and the area array CCD detector (7) is focused and position-fixed through the threads and locking nuts on the object telecentric objective (4); The area array CCD detector (7) is located at the focal plane of the object far- field objective (4); The light beam emitted by the integrating sphere light source (1) passes through the reference narrow-band filter (2), so that the effective light rays within the spectral bandwidth are transmitted, and is irradiated onto the object field diaphragm (3) to form a light spot, the light spot is incident into the object far- field objective (4), and is irradiated to the measured narrow-band filter sample (5) in the front lens barrel assembly (9) in a region, and then passes through the first lens (L1), the second lens (L2), the third lens (L3) and the fourth lens (L4) to form a collimated light beam, the collimated light beam passes through the rear lens barrel assembly (10) to focus, and is imaged on the area array CCD detector (7), and the data acquisition system (8) is used for image acquisition.

2. The apparatus for detecting uniformity of a narrow-band filter spectral space according to claim 1, wherein: The center wavelength of the reference narrow-band filter (2) is the same as that of the measured narrow-band filter sample (5), and the bandwidth of the reference narrow-band filter (2) is not less than that of the measured narrow-band filter sample (5).

3. The apparatus for detecting uniformity of a narrow-band filter spectral space according to claim 1, wherein: The area array CCD detector (7) is a frame transfer type CCD detector.

4. The apparatus for detecting uniformity of a narrow-band filter spectral space according to claim 1, wherein: The integrating sphere light source (1) uses a halogen lamp as an illumination light source.

5. The apparatus for detecting uniformity of a narrow-band filter spectral space according to claim 1, wherein: The magnification of the object far- field objective (4) is between 0.3 and 1.

5.

6. A method for detecting uniformity of a narrow-band filter spectral space, characterized by, It is applied to the uniformity detection device as claimed in claim 1, and comprises the following steps: Step 1, the data acquisition system (8) performs multiple image acquisitions on the imaging on the area array CCD detector (7), obtains a plurality of spectral response values, and then performs image averaging, background subtraction and frame transfer correction preprocessing on all the spectral response values to obtain the image gray value of the whole image plane {DN1(i,j)|i,j=1,2,…,N}, wherein DN1(i,j) represents the gray value of the i-th row and j-th column pixel; and N represents the number of pixels. Step 2, the measured narrow-band filter sample (5) is taken out from the narrow-band filter mounting assembly (6), and the axial distance between the area array CCD detector (7) and the image side vertex of the ninth lens (L10) is adjusted, so that the area array CCD detector (7) can clearly image. Step 3, the data acquisition system (8) is used for multiple image acquisitions on the imaging on the area array CCD detector (7), a plurality of spectral response values without the sample are obtained, and then image averaging, background subtraction and frame transfer correction preprocessing are performed on all the spectral response values without the sample to obtain the image gray value of the whole image plane without the sample {DN2(i,j)|i,j=1,2,…,N}, wherein DN2(i,j) represents the gray value of the i-th row and j-th column pixel without the sample. Step 4, calculating the i-th row j-th column surface uniformity of the narrow-band filter sample (5) to be tested Thus, the surface uniformity {η(i,j)|i,j=1,2,…,N} of the narrow-band filter sample (5) to be tested is obtained.

Citation Information

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