CN115421297A - Method for determining optimal focal plane position of optical system - Google Patents

Method for determining optimal focal plane position of optical system Download PDF

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CN115421297A
CN115421297A CN202211212884.8A CN202211212884A CN115421297A CN 115421297 A CN115421297 A CN 115421297A CN 202211212884 A CN202211212884 A CN 202211212884A CN 115421297 A CN115421297 A CN 115421297A
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optical system
wave aberration
variance
calculating
field
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王灵杰
于亚琼
张新
张纪鹏
赵尚男
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Changchun Institute of Optics Fine Mechanics and Physics of CAS
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Changchun Institute of Optics Fine Mechanics and Physics of CAS
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    • G02—OPTICS
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Abstract

The invention provides a method for determining the optimal focal plane position of an optical system, which comprises the following steps: s1, constructing a wave aberration model when an optical system image plane introduces an inclination amount and a defocus amount; s2, setting a truncation error delta of the defocusing amount of the image surface of the optical system according to the focal depth delta of the optical system 0 (ii) a S3, calculating the variance of wave aberration of the optical system
Figure DDA0003875630010000011
Establishing a mathematical model of the wave aberration root mean square value of the optical system; s4, constructing the wave aberration variance of the optical system
Figure DDA0003875630010000012
Equation set with first partial derivative equal to zero and calculating image plane defocusing amount delta z (ii) a S5, defocusing amount delta according to image surface z The optimal focal plane position of the optical system is calculated. According to the invention, by introducing the wavelength weight and the view field weight, a weighting function relation is established between the defocusing amount of the image surface and the imaging quality of different wavelengths and view fields of the systemThe image quality of the image plane determined by the invention can comprehensively reflect the aberration characteristic of the imaging system, thereby improving the image quality of the imaging system.

Description

Method for determining optimal focal plane position of optical system
Technical Field
The invention relates to the technical field of optical design, in particular to a method for determining the optimal focal plane position of an optical system.
Background
In the simulation design process of the imaging optical system, the position of a focal plane of the system is usually determined based on a paraxial imaging formula of Gaussian optics, and then the imaging quality of the focal plane is used as an iteration starting point of image quality evaluation of further optimization design of the optical system.
The focal plane position of the optical system determined by Gaussian optics only satisfies ideal imaging or imaging with minimum aberration on an on-axis beam, and large aberration exists for imaging an off-axis beam. Therefore, the focal plane position is not the optimal focal plane position for imaging the system, which is used for comprehensively analyzing the imaging quality of the on-axis and off-axis visual fields of the optical system.
If a field weight factor is set according to the design index requirements of the optical system, and a certain defocusing amount is introduced into the focal plane position of the optical system, the focal plane position which meets the requirements of the system on-axis and off-axis field imaging quality weighting optimization can be obtained.
Disclosure of Invention
In view of the above problems, it is an object of the present invention to provide a method for determining an optimal focal plane position of an optical system, first, constructing a wave aberration calculation model of the optical system when an image plane introduces tilt and defocus; secondly, setting a truncation error of the defocusing amount of the image surface according to the system focal depth; then, according to a relational expression of the wavefront variance of the optical system, the image plane inclination factor and the defocus factor, an equation set of which the first-order partial derivative is equal to zero is constructed, and the equation set is solved by adopting a least square method; and finally, obtaining the defocusing amount corresponding to the optimal focal plane position of the system. By the method, the focal plane position with the optimal weighting of the imaging quality of the on-axis field and the off-axis field of view of the imaging system can be obtained, and the image quality of the imaging system is improved.
In order to achieve the purpose, the invention adopts the following specific technical scheme:
the invention provides a method for determining the optimal focal plane position of an optical system, which comprises the following steps:
s1, constructing a wave aberration model when an optical system image plane introduces an inclination amount and a defocus amount;
s2, setting a truncation error delta of the defocusing amount of the image surface of the optical system according to the focal depth delta of the optical system 0 ：
δ 0 ＝C·δ (4)
Wherein the content of the first and second substances,
c is a scale factor;
s3, calculating the variance of wave aberration of the optical system
Figure BDA0003875626990000021
Establishing a mathematical model of the wave aberration root mean square value of the optical system;
s4, constructing the wave aberration variance of the optical system
Figure BDA0003875626990000022
Equation set with first partial derivative equal to zero and calculating image plane defocusing amount delta z ；
S5, defocusing amount delta according to image surface z The optimal focal plane position of the optical system is calculated.
Preferably, the optical system wave aberration calculation model is:
Figure BDA0003875626990000023
wherein the content of the first and second substances,
w (x, y) is the wave aberration of the optical system when the optical system introduces the inclination amount and the defocus amount;
W 0 (x, y) is the original wave aberration of the optical system;
x, y and z are coordinates of the light rays in the optical system on the exit pupil surface respectively;
r is the radius of the exit pupil sphere;
δ x ，δ y the inclination amounts of the image plane along the directions of the x axis and the y axis are respectively;
δ z the defocusing amount of the image surface along the z-axis direction is obtained;
λ is the wavelength;
calculating the wave aberration root mean square value RMS according to the wave aberration W (x, y):
Figure BDA0003875626990000024
wherein the content of the first and second substances,
n is the number of rays;
calculating the wave aberration variance H according to the wave aberration root mean square value RMS:
H＝(RMS) 2 (3)。
preferably, the number of rays n ranges from: 400 to 16000; the scale factor C preferably has a value range of: 0.01 to 1.
Preferably, step S3 comprises the following sub-steps:
s31, calculating the wavelength weight mu i And field weight K j ；
Wavelength weight mu i The calculation formula of (2) is as follows:
Figure BDA0003875626990000031
wherein, the first and the second end of the pipe are connected with each other,
i＝1…m；
μ i weight of the ith wavelength;
λ i is the ith wavelength;
Figure BDA0003875626990000032
is the weighting factor of the ith wavelength.
Field of view weight K j The calculation formula of (2) is as follows:
Figure BDA0003875626990000033
wherein, the first and the second end of the pipe are connected with each other,
j＝1…N；
K j is the field weight;
Figure BDA0003875626990000034
a weight factor for the jth field of view;
N j the number of trace rays for the jth field of view.
Number of rays N traced in jth field of view j Comprises the following steps:
Figure BDA0003875626990000035
wherein the content of the first and second substances,
n i the number of rays traced by the ith wavelength for the jth field of view;
m is the total number of wavelengths of the optical system;
s32, weighting mu according to wavelength i And field weight K j And calculating a model of the wave aberration root mean square value of the optical system.
Preferably, step S32 comprises the following sub-steps:
s321, calculating wave aberration variance V of single field of view j ：
Figure BDA0003875626990000041
Wherein, the first and the second end of the pipe are connected with each other,
V j a wave aberration variance for a jth field of view of the optical system;
j =1 \ 8230, N, N is total field of view of the optical system;
H i is a wavelength lambda i The variance of the wave aberration;
μ i is a wavelength lambda i The weight of (c);
i =1 \ 8230m, total number of wavelengths of m, m optical system;
s322, establishing wave aberration variance under single field of view of the optical system
Figure BDA0003875626990000048
Functional relationship with the variance of the wave aberration of the N fields of view:
Figure BDA0003875626990000042
s323, calculating the root mean square value of the wave aberration of the optical system:
Figure BDA0003875626990000043
preferably, the image plane defocus amount δ z The calculation process of (2) is as follows:
s41, an equation set with the first-order partial derivative of the wave aberration variance of the optical system equal to zero is constructed.
The wave aberration variance of the optical system can be expressed as a multi-element function of the X-direction inclination of the image plane, the Y-direction inclination of the image plane and the Z-direction defocus of the image plane corresponding to N fields:
Figure BDA0003875626990000044
wherein the content of the first and second substances,
Figure BDA0003875626990000045
the inclination amount of the j field image surface along the X-axis direction;
Figure BDA0003875626990000046
is the inclination of the jth field image plane in the Y-axis direction;
δ z the defocusing amount of the image surface along the Z-axis direction;
s42, calculating the variance of wave aberration
Figure BDA0003875626990000047
Respectively solving first-order partial derivatives of all variables, and respectively enabling the values to be equal to 0;
thereby establishing an equation system with the first partial derivative of the variance of the wave aberration of the optical system equal to zero:
Figure BDA0003875626990000051
s43, calculating the defocusing amount delta of the image plane by a least square method z 。
Preferably, step S5 comprises the following sub-steps:
s51, determining the defocusing amount delta of the image surface z Truncation error delta less than or equal to image plane defocus amount 0 Then, go to step S52;
δ z ≤δ 0 (13)
if the image plane is out of focus delta z Truncation error delta larger than image plane defocusing amount 0 And repeating the step 3 and the step 4 until the image plane defocusing amount delta z Truncation error delta less than or equal to image plane defocus amount 0 If yes, go to step S52;
s52, calculating the optimal focal plane position of the optical system;
calculating the optimal focal plane position of the optical system:
Figure BDA0003875626990000052
wherein the content of the first and second substances,
Figure BDA0003875626990000053
the defocus amount required to be introduced for obtaining the optimal focal plane position;
Figure BDA0003875626990000054
the image plane defocusing amount obtained by solving the formula (12) at the kth time;
k =1 \8230S, S is the number of times equation (12) is solved when equation (13) holds.
Compared with the prior art, the method has the advantages that the wavelength weight and the view field weight are introduced, and the weighting function relationship is established between the defocusing amount of the image surface and the imaging quality of different wavelengths and view fields of the system, so that the image quality of the image surface determined by the method can comprehensively reflect the aberration characteristic of the imaging system, and the image quality of the imaging system is improved.
Drawings
Fig. 1 is a schematic flowchart of a method for determining an optimal focal plane position of an optical system according to an embodiment of the present invention.
Fig. 2 is a block diagram of a process for determining an optimal focal plane position of an optical system according to an embodiment of the present invention.
Detailed Description
Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In the following description, the same reference numerals are used for the same blocks. In the case of the same reference numerals, their names and functions are also the same. Therefore, detailed description thereof will not be repeated.
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not to be construed as limiting the invention.
Fig. 1 is a flowchart illustrating a method for determining an optimal focal plane position of an optical system according to an embodiment of the present invention.
Fig. 2 is a block diagram illustrating a procedure of determining an optimal focal plane position of an optical system according to an embodiment of the present invention.
As shown in fig. 1-2, the method for determining the optimal focal plane position of the optical system according to the embodiment of the present invention includes the following steps:
s1, constructing a wave aberration model when an optical system image plane introduces inclination and defocusing.
When the image plane introduces the inclination and the defocus, the wave aberration calculation model of the optical system is shown as the formula (1):
Figure BDA0003875626990000061
wherein, the first and the second end of the pipe are connected with each other,
w (x, y) is the wave aberration of the optical system when the amount of tilt and the amount of defocus are introduced;
W 0 (x, y) isThe original wave aberration of the optical system;
x, y and z are coordinates of the light rays on the exit pupil surface respectively;
r is the exit pupil spherical radius;
δ x ，δ y the inclination amounts in the x-axis and y-axis directions of the image plane are respectively;
δ z the defocusing amount of the image surface along the z-axis direction is obtained;
λ is the wavelength.
Calculating the wave aberration root mean square value RMS according to the wave aberration W (x, y):
Figure BDA0003875626990000071
wherein, the first and the second end of the pipe are connected with each other,
RMS is the root mean square value of the wave aberration;
n is the number of tracking rays;
w is the wave aberration of the optical system when the amount of tilt and the amount of defocus are introduced.
When the number of rays n is larger, the result of obtaining the wave aberration value W (x, y) is more accurate, but the calculation time increases, and the range of the number of rays n is preferably: 400 to 16000.
In one embodiment provided by the present invention: n is 3216.
Calculating the wave aberration variance H according to the wave aberration root mean square value RMS:
H＝(RMS) 2 (3)
s2, setting truncation error delta of image plane defocusing amount of optical system 0 。
According to the focal depth of the optical system, the truncation error delta of the defocusing amount of the image surface is set 0 As shown in equation (4):
δ 0 ＝C·δ (4)
wherein the content of the first and second substances,
delta is the optical system focal depth;
δ 0 the truncation error of the defocusing amount of the image surface of the optical system is obtained;
c is a scale factor and is used for controlling the iteration precision, and the value range of C is preferably as follows: 0.01 to 1.
In one embodiment provided by the invention: c is 0.1, and the truncation error delta of the defocusing amount of the image surface 0 Set at 2.7 microns.
S3, calculating the variance of wave aberration of the optical system
Figure BDA0003875626990000072
And establishing a mathematical model of the wave aberration root mean square value of the optical system.
Step S3 includes the following substeps:
s31, calculating the wavelength weight mu i And field weight K j 。
For a given optical system, the system parameters include m wavelengths and a weighting factor for each wavelength, and N fields of view and a weighting factor for each field of view.
In one embodiment provided by the present invention: m is 3, N is 3.
The wavelengths and wavelength weighting factors, field of view and field of view weighting factor settings are shown in table 1.
Table 1: wavelength and wavelength weight factor, field of view and field of view weight factor parameter settings
Figure BDA0003875626990000081
Wavelength weight mu i The calculation formula (2) is shown in formula (5):
Figure BDA0003875626990000082
wherein, the first and the second end of the pipe are connected with each other,
i＝1…m；
μ i is the weight of the ith wavelength;
λ i is the ith wavelength;
Figure BDA0003875626990000083
is the weighting factor of the ith wavelength.
Field weight K j Is shown in equation (6):
Figure BDA0003875626990000084
wherein, the first and the second end of the pipe are connected with each other,
j＝1…N；
K j is the field of view weight;
Figure BDA0003875626990000085
a weight factor for the jth field of view;
N j the number of trace rays for the jth field of view.
Number of rays N for jth field of view trace j Is calculated as shown in equation (7):
Figure BDA0003875626990000086
wherein the content of the first and second substances,
N j the number of rays traced for the jth field of view of the optical system;
n i the number of rays traced by the ith wavelength for the jth field of view;
and m is the total number of wavelengths of the optical system.
It should be noted that the wavelength weighting factor
Figure BDA0003875626990000091
And field weight factor
Figure BDA0003875626990000092
Is an inherent parameter of the system, and the wavelength weight mu i And field weight K j Is calculated by the method of the invention.
S32, weighting mu according to wavelength i And field weight K j And calculating a model of the wave aberration root mean square value of the optical system.
Step S32 includes the following substeps:
s321, calculating wave aberration variance V of single view field j ：
Figure BDA0003875626990000093
Wherein the content of the first and second substances,
V j a wave aberration variance for a jth field of view of the optical system;
j =1 \ 8230, N, N is the total number of fields of view of a given optical system;
H i is a wavelength lambda i The variance of the wave aberration;
μ i is the wavelength lambda i The weight of (c);
i =1 \ 8230m, m gives the total number of wavelengths of the optical system.
S322, establishing a functional relation between the wave aberration variance under a single field of view of the optical system and the wave aberration variances of the N field of view:
Figure BDA0003875626990000094
wherein the content of the first and second substances,
Figure BDA0003875626990000095
is the wave aberration variance of the optical system;
V j a wave aberration variance for a jth field of view;
K j is the weight of the jth field of view;
j =1 \ 8230n, N being the total number of fields of view for a given optical system.
S323, calculating the root mean square value of wave aberration of the optical system:
Figure BDA0003875626990000096
wherein the content of the first and second substances,
Figure BDA0003875626990000101
the wave aberration root mean square value of the optical system;
Figure BDA0003875626990000102
is the wave aberration variance of the optical system.
S4, constructing the wave aberration variance of the optical system
Figure BDA0003875626990000103
Equation set with first partial derivative equal to zero and calculating image plane defocusing amount delta z 。
Defocusing amount delta of image surface z The calculation process of (2) is as follows:
s41, an equation set with the first-order partial derivative of the wave aberration variance of the optical system equal to zero is constructed.
According to the optical theory, the wave aberration variance of the optical system can be expressed as a multi-element function of the image plane X-direction inclination, the image plane Y-direction inclination and the image plane Z-direction defocus corresponding to N fields, as shown in formula (11):
Figure BDA0003875626990000104
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003875626990000105
is the variance of the wave aberration of the optical system;
Figure BDA0003875626990000106
the inclination of the image surface in the X direction of the jth field of view is set;
Figure BDA0003875626990000107
is the Y-direction inclination of the jth field-of-view image plane;
j =1 \ 8230n, N being the total number of fields of view of a given optical system;
δ z is the defocus amount of the image plane in the Z direction.
S42, calculating the wave aberration variance in the formula (11)
Figure BDA0003875626990000108
The first partial derivatives are calculated for the respective variables, and the values are all equal to 0.
Thereby establishing a system of equations in which the first partial derivative of the variance of the system wave aberration is equal to zero, as shown in equation (12):
Figure BDA0003875626990000109
s43, calculating the defocusing amount delta of the image plane by a least square method z 。
S5, defocusing amount delta according to image surface z The optimal focal plane position of the optical system is calculated.
Step S5 includes the following substeps:
s51, determining the defocusing amount delta of the image surface z Truncation error delta less than or equal to image plane defocus 0 Then, go to step S52;
δ z ≤δ 0 (13)
wherein, the first and the second end of the pipe are connected with each other,
δ z the image plane defocus amount solved for the formula (12);
δ 0 is a truncation error of the set image plane defocus amount.
If the image plane is out of focus delta z Truncation error delta larger than image plane defocusing amount 0 Then the image plane is defocused by delta z Transmitting to the image plane defocusing amount position of a given optical system, and repeating the steps 3 and 4 until the image plane defocusing amount delta z Truncation error delta less than or equal to image plane defocus amount 0 Then, the process proceeds to step S52.
And S52, calculating the optimal focal plane position of the optical system.
The image plane defocusing amount delta obtained by solving the formula (12) for the kth time z Record as
Figure BDA0003875626990000111
Calculating the optimal focal plane position of the optical system:
Figure BDA0003875626990000112
wherein the content of the first and second substances,
Figure BDA0003875626990000113
the defocus quantity required to be introduced for obtaining the optimal focal plane position;
Figure BDA0003875626990000114
the image plane defocusing amount obtained by solving the formula (12) at the kth time;
k =1 \ 8230S, S is the number of times equation (12) is solved when equation (13) holds.
The invention uses MATLAB 2020b platform to complete simulation on Inter (R) PC with CPU 2.50GHz, 1lg. The optical system parameters of the simulation example are shown in table 1, the surface type parameters are shown in table 2, the system focal depth delta is 27.31 microns, and the image plane defocus truncation error delta is 0 Set at 2.7 microns.
Table 2: surface profile parameter of optical system
Figure BDA0003875626990000115
Figure BDA0003875626990000121
Table 3: the focal plane position of the optical system provided by the invention is compared with the wavefront root mean square value result of each field of view of the focal plane position determined by Gaussian optics
Figure BDA0003875626990000122
The ratio of the wavefront root mean square value of each field of view at the focal plane position determined by the invention and the focal plane position determined by Gaussian optics is shown in Table 3. It can be derived from table 3 that the system wavefront root mean square value on the focal plane determined by the present invention is significantly smaller than the system wavefront root mean square value on the focal plane determined by gaussian optics, i.e. the focal plane image quality determined by the present invention is significantly better than the focal plane image quality determined by gaussian optics.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.
The above embodiments of the present invention should not be construed as limiting the scope of the present invention. Any other corresponding changes and modifications made according to the technical idea of the present invention should be included in the protection scope of the claims of the present invention.

Claims (7)

1. A method for determining an optimal focal plane position of an optical system, comprising the steps of:
s1, constructing a wave aberration model when an inclination amount and a defocusing amount are introduced into an optical system image plane;
s2, setting a truncation error delta of the defocusing amount of the image surface of the optical system according to the focal depth delta of the optical system 0 ：
δ 0 ＝C·δ (4)
Wherein the content of the first and second substances,
c is a scale factor;
s3, calculating the variance of wave aberration of the optical system
Figure FDA0003875626980000011
Establishing a mathematical model of the wave aberration root mean square value of the optical system;
s4, constructing an optical system about the wave aberration variance
Figure FDA0003875626980000012
System of equations with first partial derivative equal to zeroAnd calculating the defocusing amount delta of the image surface z ；
S5, defocusing amount delta according to the image plane z Calculating an optimal focal plane position of the optical system.
2. The method for determining the best focal plane position of an optical system according to claim 1, wherein the optical system wave aberration calculation model is:
Figure FDA0003875626980000013
wherein the content of the first and second substances,
w (x, y) is the wave aberration of the optical system when the optical system introduces the inclination amount and the defocus amount;
W 0 (x, y) is the original wave aberration of the optical system;
x, y and z are coordinates of the light rays in the optical system on an exit pupil surface respectively;
r is the radius of the exit pupil sphere;
δ x ，δ y the inclination amounts of the image surface along the directions of an x axis and a y axis are respectively;
δ z the defocusing amount of the image surface along the z-axis direction is obtained;
λ is the wavelength;
calculating a wave aberration root mean square value RMS according to the wave aberration W (x, y):
Figure FDA0003875626980000014
wherein the content of the first and second substances,
n is the number of the light rays;
calculating the wave aberration variance H according to the wave aberration root mean square value RMS:
H＝(RMS) 2 (3)。
3. the method of claim 2, wherein the number of light rays n ranges from: 400 to 16000; the value range of the scale factor C is preferably as follows: 0.01 to 1.
4. The method for determining the best focal plane position of an optical system according to claim 2, wherein the step S3 comprises the following sub-steps:
s31, calculating the wavelength weight mu i And field weight K j ；
The wavelength weight mu i The calculation formula of (c) is:
Figure FDA0003875626980000021
wherein, the first and the second end of the pipe are connected with each other,
i＝1…m；
μ i weight of the ith wavelength;
λ i is the ith wavelength;
Figure FDA0003875626980000022
a weight factor for the ith wavelength;
the field weight K j The calculation formula of (c) is:
Figure FDA0003875626980000023
wherein the content of the first and second substances,
j＝1…N；
K j is the field of view weight;
Figure FDA0003875626980000024
a weight factor for the jth field of view;
N j the number of trace rays for the jth field of view;
number of rays N traced in jth field of view j Comprises the following steps:
Figure FDA0003875626980000025
wherein the content of the first and second substances,
n i the number of rays traced by the ith wavelength for the jth field of view;
m is the total number of wavelengths of the optical system;
s32, weighting mu according to wavelength i And field weight K j And calculating a model of the wave aberration root mean square value of the optical system.
5. The method for determining the best focal plane position of an optical system according to claim 4, wherein the step S32 comprises the following sub-steps:
s321, calculating wave aberration variance V of single view field j ：
Figure FDA0003875626980000031
Wherein, the first and the second end of the pipe are connected with each other,
V j a wave aberration variance for a jth field of view of the optical system;
j =1 \ 8230N, N is the total field of view of the optical system;
H i is the wavelength lambda i The variance of the wave aberration;
μ i is a wavelength lambda i The weight of (c);
i = 1\8230m, the total number of wavelengths of the optical system m;
s322, establishing wave aberration variance under single field of view of the optical system
Figure FDA0003875626980000032
Functional relationship with the variance of the wave aberration of the N fields of view:
Figure FDA0003875626980000033
s323, calculating the root mean square value of the wave aberration of the optical system:
Figure FDA0003875626980000034
6. the method for determining the best focus plane position of an optical system according to claim 5, wherein the image plane defocus amount δ z The calculation process of (2) is as follows:
s41, constructing an equation set of which the first-order partial derivative of the wave aberration variance of the optical system is equal to zero;
the wave aberration variance of the optical system can be expressed as a multi-element function of the X-direction inclination of the image plane, the Y-direction inclination of the image plane and the Z-direction defocus of the image plane corresponding to the N fields:
Figure FDA0003875626980000035
wherein the content of the first and second substances,
Figure FDA0003875626980000036
the inclination amount of the jth view field image surface along the X-axis direction is shown;
Figure FDA0003875626980000037
is the inclination of the jth field image plane in the Y-axis direction;
δ z the defocusing amount of the image surface along the Z-axis direction;
s42, converting the wave aberration variance
Figure FDA0003875626980000041
Respectively solving first-order partial derivatives of all the variables, and respectively enabling the values to be equal to 0;
thereby establishing a system of equations in which the first partial derivative of the variance of the wave aberration of the optical system is equal to zero:
Figure FDA0003875626980000042
s43, calculating the defocusing amount delta of the image plane by a least square method z 。
7. The method for determining the best focal plane position of an optical system according to claim 6, wherein the step S5 comprises the sub-steps of:
s51, if the image plane defocuses by an amount delta z Truncation error delta less than or equal to the defocusing amount of the image surface 0 Then, go to step S52;
δ z ≤δ 0 (13)
if the defocusing amount delta of the image surface z Truncation error delta larger than defocusing amount of image surface 0 Repeating the step 3 and the step 4 until the image plane defocusing amount delta z Truncation error delta less than or equal to image plane defocus 0 If yes, the flow proceeds to step S52;
s52, calculating the optimal focal plane position of the optical system;
calculating the optimal focal plane position of the optical system:
Figure FDA0003875626980000043
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003875626980000044
the defocus amount required to be introduced in the optimal focal plane position is obtained;
Figure FDA0003875626980000045
the image plane defocusing amount obtained by solving the formula (12) at the kth time;
k =1 \8230S, S is the number of times the equation (12) is solved when the equation (13) holds.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117689892A (en) * 2024-02-02 2024-03-12 中国科学院长春光学精密机械与物理研究所 Remote sensing image focal plane discriminating method

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117689892A (en) * 2024-02-02 2024-03-12 中国科学院长春光学精密机械与物理研究所 Remote sensing image focal plane discriminating method
CN117689892B (en) * 2024-02-02 2024-04-09 中国科学院长春光学精密机械与物理研究所 Remote sensing image focal plane discriminating method

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