CN112394508A - Debugging method based on second-order sensitivity matrix method - Google Patents
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Abstract
The invention discloses an assembling and adjusting method based on a second-order sensitivity matrix method. And repeating the steps to obtain a plurality of groups of maladjustment errors and corresponding Zernike coefficients, and then obtaining a curve relation function of the maladjustment errors and the Zernike coefficients according to a least square method principle. And then solving a second order derivative about the detuning amount by using the obtained curve function to further obtain a second order sensitivity matrix, and finally guiding and adjusting the off-axis optical system by using the second order sensitivity matrix. The invention can be suitable for a large error range, has higher precision than the traditional sensitivity matrix, can be better used for the actual assembly and adjustment engineering, and improves the final imaging quality of the optical system.
Description
Technical Field
The invention belongs to the field of optical system installation and debugging, and particularly relates to an installation and debugging method based on a second-order sensitivity matrix method.
Background
In the fields of astronomical observation, free space optical communication, remote sensing to the ground and the like, a large-aperture refraction and reflection type optical system has chromatic aberration and has a secondary spectrum, so that certain limitation is caused. The reflection type optical system has no chromatic aberration, can perform wide-spectrum imaging, has compact optical path structure, and can be widely applied by adopting a free-form surface as a reflecting surface. Further, in the reflective optical system, it is applied to astronomy because the off-axis optical system has a smaller obscuration ratio and a larger amount of light passing. However, in the adjustment of the off-axis optical system, there is a possibility that each lens has an error of six degrees of freedom due to the asymmetry of the lens, which also increases the difficulty of the adjustment process. How to quickly and accurately determine the alignment error of the lens is always a problem to be solved urgently in the installation and adjustment.
Aiming at the practical engineering problem, related scientific research personnel also carry out certain research and develop the computer-aided debugging method with the highest use frequency at present. This installation and adjustment process requires two steps: first, coarse adjustment is performed. The coarse adjustment stage is mainly to adjust the alignment error of the off-axis optical system to a small enough range according to the experience of the adjustment personnel. And secondly, the fine tuning is guided by solving a sensitivity matrix. The solving of the sensitivity matrix firstly needs to establish an off-axis reflective optical system model by using optical simulation software, and because the aberration of the optical system can be expressed by using Zernike polynomial coefficients, the change amount of the corresponding Zernike coefficients can be obtained by adding alignment errors to the model. And then drawing a relation function according to the added alignment error and the coefficient change of the Zernike polynomial, and then obtaining a corresponding fitting function by using a least square method, wherein the alignment error is reduced to a smaller range by early coarse adjustment, so that the linear relation between the aberration and the detuning error of the optical system can be assumed, a sensitivity matrix of the aberration and the detuning amount is solved, and the sensitivity matrix is used for guiding fine adjustment. However, this method is not suitable for settings within a large error range.
Disclosure of Invention
The invention aims to provide a method for establishing the relation between the alignment error of a primary mirror and a secondary mirror of an off-axis reflective optical system and various aberrations based on a second-order sensitivity matrix principle, so that the adjustment efficiency of a system lens is accelerated, and higher adjustment accuracy and better adjustment effect are obtained.
The technical scheme for realizing the purpose of the invention is as follows: a second-order sensitivity matrix method-based adjustment method is used for alignment correction of primary and secondary mirrors of an off-axis reflective optical system, and comprises the following specific steps:
step one, establishing an optical system model and optimizing:
and sequentially inputting the structural parameters of the off-axis reflective optical system into optical simulation software Zemax, establishing an optical system model, and optimizing non-key structural parameters of the optical system until the optical system has the optimal imaging quality, wherein the secondary mirror is regarded as an ideal position.
Step two, acquiring the Zernike coefficient
First, the first eight Zernike coefficients Z of the ideal position in the optical system model are recorded0 nWherein n is more than or equal to 1 and less than or equal to 8. Then changing the eccentricity and inclination of the secondary mirror in the X and Y directions respectively by (d)1 xd1 yt1 xt1 y) Representing four misadjustment errors between the primary mirror and the secondary mirror, and then obtaining the front eight terms Z of Zernike through aberration coefficients in a Zemax analysis function1 nWherein n is more than or equal to 1 and less than or equal to 8;
repeating the steps to obtain N groups of Zernike coefficients Zm nWherein m is more than or equal to 1 and less than or equal to N, and N is more than or equal to 1 and less than or equal to 8;
step three, calculating the change amount of the Zernike
The obtained N groups of Zernike coefficients Zm nSubtracting the Zernike coefficients Z at the ideal positions, respectively0 nTo obtain the change amount of the Zernike coefficient, namely, Delta Zm n＝Zm n-Z0 nWherein m is more than or equal to 1 and less than or equal to N, and N is more than or equal to 1 and less than or equal to 8;
step four, drawing a relation curve of aberration and detuning quantity
And then, drawing a relation curve graph of the change quantity and the detuning quantity of the Zernike coefficient by adopting a mathematical drawing tool. Because the system aberration can be represented by Zernike coefficients one by one, the obtained curve graph of the relationship between the variable quantity and the detuning quantity of the Zernike coefficients is the curve graph of the relationship between the aberration and the detuning quantity;
step five relation function fitting
Then fitting a relational function expression of aberration and maladjustment error by adopting a least square method;
step six first order and second order sensitivity matrix solving
According to the obtained specific expression of the relation function, second derivative solving about the detuning amount is selected to be carried out on the relation function, and then a second-order sensitivity matrix is obtained;
step seven calculation of the amount of detuning
In actual assembly and adjustment, a wave-front sensor is used for measuring Zernike coefficients, the coefficients are respectively differed with the Zernike coefficients at the ideal position of the simulation model in zemax to obtain a Zernike coefficient change quantity, then the detuning quantity of the off-axis optical system is reversely solved by the previously obtained second-order sensitivity matrix, and finally the assembly and adjustment are guided according to the reversely solved detuning quantity.
Further, in the step one, the off-axis reflective telescope system is a telescope system in which the entrance pupil is deviated from the main optical axis, but the off-axis reflective telescope system is not limited to the off-axis reflective telescope system, and may be a series of telescope systems such as an on-axis refractive telescope system.
Further, the off-axis quantity d of the primary mirror and the secondary mirror in the horizontal axis and the vertical axis directions in the step twom xdm yThe displacement of the secondary mirror relative to the primary mirror position in the X-axis and y-axis directions deviating from the primary axis is respectively, the direction of the secondary mirror is based on the direction of a Cartesian coordinate system, and the Cartesian coordinate system is set as follows: the optical axis is the Z axis, and the light propagation direction is positive; the Y axis and the Z axis form a meridian plane, and the upward direction is the positive direction of the Y axis; the X axis and the Z axis form a sagittal plane, and the outward direction is the positive direction of the X axis; amount of inclination tm xtm yThe angles of rotation of the secondary mirror about the X-axis and about the Y-axis, respectively, with respect to the primary mirror.
Further, in the second step, the zernike coefficients are: w (ρ, θ) ═ A0+A1*ρcosθ+A2*ρsinθ+A3*(2ρ2-1)+A4*ρ2cos 2θ+A5*ρ2sin 2θ+A6*(3ρ2-2)ρcosθ+A7*(3ρ2-2) ρ sin θ, A in the formula0，A1，A2，A3，A4，A5，A6，A7I.e. the first eight zernike coefficients.
Further, the zernike coefficients of the first eight terms in the steps two and five may be not limited to the first eight terms, but may also be the first nine terms, and the first ten terms and the like may accurately represent the zernike coefficients of the first n (n is 8, 9, 10.) terms of the wavefront aberration.
Further, the zernike coefficient difference in step three refers to the difference between the wave aberration with alignment error and the system inherent wave aberration, which represents the amount of change in the system wave aberration caused by the misalignment amount.
Further, the relationship between the zernike coefficients and the aberrations described in step four may be a one-to-one mapping relationship between the zernike coefficients and the system wavefront aberrations, such as the first term representing the optical path difference, the second term representing the tilt amount, the fourth term representing the defocus amount, the fifth sixth term representing the astigmatism, and the seventh term representing the coma.
Further, the least square fitting in step five is based on the differences Δ Z between N sets of Zernike coefficientsm nAnd correspondingly four d1 xd1 yt1 xt1 yAnd fitting the Zernike coefficients and the alignment detuning amount by a multi-order function by using a least square method.
Further, the wavefront sensor described in step six may be an optical sensing device that converts the system wavefront aberrations into those characterized by a zernike polynomial.
The principle of the invention is as follows:
1. from the zernike polynomials: any integrable function within the unit circle can be represented by Vpq(x，y)＝Vpq(ρ，θ)＝Rpq(ρ)ejqθTo indicate that the complex-valued function set has completeness and orthogonality. Wherein R ispq(ρ) can be expressed as:
expanding the formula into a power series form under polar coordinates
U in the formula0...UnAre coefficients of zernike polynomials, which can be used to represent the wavefront aberrations of an optical system.
2. Assuming that there is some relationship between the zernike coefficients and the amount of detuning, we find that there is a linear relationship, but some are second order non-linear relationships, between some of the zernike coefficients and the amount of detuning by using zemax simulations. We therefore assume that Δ Z is a '× Δ B + a × (Δ B × Δ B), where Δ Z represents the amount of change in the zernike coefficient, Δ B represents the amount of detuning of the system, a' represents the first-order sensitivity, and a "represents the second-order sensitivity.
3. When the relationship between the Zernike coefficient and the detuning amount is fitted, an overdetermined equation set is formed because the acquired data set N is more than 8 unknown amounts, and a least square method can be selectively applied to solve the overdetermined equation set. After the least square method is used for obtaining the variation of the detuning quantity and the Zernike coefficient, a corresponding relation curve expression can be obtained by a polynomial fitting method, and further a corresponding first-order sensitivity matrix and a corresponding second-order sensitivity matrix can be obtained. In addition, in the adjustment, the change amount of the zernike coefficient needs to be obtained first. Therefore, the wavefront sensor is required to obtain the Zernike coefficient for representing the wavefront aberration, and then the systematic maladjustment error can be obtained according to the inverse solution of the second-order sensitivity matrix.
Compared with the prior art, the invention has the advantages that:
(1) the method has simple flow and does not need to perform rough installation and adjustment;
(2) the method does not need the linear relation between the Zernike coefficient and the detuning quantity, and the fitting precision of the nonlinear relation is high;
(3) the method has simple light path and less detection equipment.
Drawings
FIG. 1 is a flow chart of an installation and debugging method based on a second-order sensitivity matrix method of the invention;
FIG. 2 is a graph of Zernike coefficients versus off-axis error in the X-axis direction;
FIG. 3 is a graph of Zernike coefficients versus off-axis error in the Y-axis direction;
FIG. 4 is a graph of Zernike coefficients versus tilt error in the X-axis direction;
FIG. 5 is a graph of Zernike coefficients versus tilt error in the Y-axis direction.
Detailed Description
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
The invention relates to an adjusting method based on a second-order sensitivity matrix method, the whole method flow is shown in figure 1, and the following detailed description is developed:
step one, establishing an optical system model and optimizing:
and sequentially inputting the structural parameters of the off-axis reflective optical system into optical simulation software Zemax, establishing an optical system model, and optimizing non-key structural parameters of the optical system until the optical system has the optimal imaging quality, wherein the secondary mirror is regarded as an ideal position.
Step two, acquiring the Zernike coefficient
First, the first eight Zernike coefficients Z of the ideal position in the optical system model are recorded0 nWherein n is more than or equal to 1 and less than or equal to 8. Then changing the eccentricity and inclination of the secondary mirror in the X and Y directions respectively by (d)1 xd1 yt1 xt1 y) Representing four misadjustment errors between the primary mirror and the secondary mirror, and then obtaining the front eight terms Z of Zernike through aberration coefficients in a Zemax analysis function1 nWherein n is more than or equal to 1 and less than or equal to 8;
repeating the above steps to obtain N groups of glazeCoefficient of nicotinic Zm nWherein m is more than or equal to 1 and less than or equal to N, and N is more than or equal to 1 and less than or equal to 8;
step three, calculating the change amount of the Zernike
The obtained N groups of Zernike coefficients Zm nSubtracting the Zernike coefficients Z at the ideal positions, respectively0 nTo obtain the change amount of the Zernike coefficient, namely, Delta Zm n＝Zm n-Z0 nWherein m is more than or equal to 1 and less than or equal to N, and N is more than or equal to 1 and less than or equal to 8;
step four, drawing a relation curve of aberration and detuning quantity
And then, drawing a relation curve graph of the change quantity and the detuning quantity of the Zernike coefficient by adopting a mathematical drawing tool. Because the system aberration can be represented by Zernike coefficients one by one, the obtained curve graph of the relationship between the variable quantity of the Zernike coefficients and the detuning quantity is the curve graph of the relationship between the aberration and the detuning quantity. Wherein FIG. 2 shows Zernike coefficients plotted against the amount of off-axis X-axis; FIG. 3 shows Zernike coefficients plotted against Y-axis off-axis amount; FIG. 4 shows a graph of Zernike coefficients versus the amount of X-axis tilt; fig. 5 shows a graph of the zernike coefficient versus the amount of Y-axis tilt. (ii) a
Step five relation function fitting
Then fitting a relational function expression of aberration and maladjustment error by adopting a least square method;
step six first order and second order sensitivity matrix solving
According to the obtained specific expression of the relation function, second derivative solving about the detuning amount is selected to be carried out on the relation function, and then a second-order sensitivity matrix is obtained;
step seven calculation of the amount of detuning
In actual assembly and adjustment, a wave-front sensor is used for measuring Zernike coefficients, the coefficients are respectively differed with the Zernike coefficients at the ideal position of the simulation model in zemax to obtain a Zernike coefficient change quantity, then the detuning quantity of the off-axis optical system is reversely solved by the previously obtained second-order sensitivity matrix, and finally the assembly and adjustment are guided according to the reversely solved detuning quantity.
Claims (9)
1. A debugging method based on a second-order sensitivity matrix method is characterized by comprising the following steps:
step one, establishing an optical system model and optimizing:
sequentially inputting structural parameters of the off-axis reflective optical system into optical simulation software Zemax, establishing an optical system model, and optimizing non-key structural parameters of the optical system until the optical system has the optimal imaging quality, wherein the secondary mirror is regarded as an ideal position;
step two, acquiring the Zernike coefficient
First, the first eight Zernike coefficients Z of the ideal position in the optical system model are recorded0 nWherein n is more than or equal to 1 and less than or equal to 8, and then changing the eccentricity value and the inclination value of the secondary mirror in the X and Y axis directions respectively by using (d)1 x d1 y t1 x t1 y) Representing four misadjustment errors between the primary mirror and the secondary mirror, and then obtaining the front eight terms Z of Zernike through aberration coefficients in a Zemax analysis function1 nWherein n is more than or equal to 1 and less than or equal to 8;
repeating the steps to obtain N groups of Zernike coefficients Zm nWherein m is more than or equal to 1 and less than or equal to N, and N is more than or equal to 1 and less than or equal to 8;
step three, calculating the change amount of the Zernike
The obtained N groups of Zernike coefficients Zm nSubtracting the Zernike coefficients Z at the ideal positions, respectively0 nTo obtain the change amount of the Zernike coefficient, namely, Delta Zm n＝Zm n-Z0 nWherein m is more than or equal to 1 and less than or equal to N, and N is more than or equal to 1 and less than or equal to 8;
step four, drawing a relation curve of aberration and detuning quantity
Then, a mathematical drawing tool is adopted to draw a relation curve graph of the change quantity and the detuning quantity of the Zernike coefficient, and the system aberration can be represented by the Zernike coefficients one by one, so that the obtained relation curve graph of the change quantity and the detuning quantity of the Zernike coefficient is the relation curve graph of the aberration and the detuning quantity;
step five relation function fitting
Then fitting a relational function expression of aberration and maladjustment error by adopting a least square method;
step six first order and second order sensitivity matrix solving
According to the obtained specific expression of the relation function, second derivative solving about the detuning amount is selected to be carried out on the relation function, and then a second-order sensitivity matrix is obtained;
step seven calculation of the amount of detuning
In actual assembly and adjustment, a wave-front sensor is used for measuring Zernike coefficients, the coefficients are respectively differed with the Zernike coefficients at the ideal position of the simulation model in zemax to obtain a Zernike coefficient change quantity, then the detuning quantity of the off-axis optical system is reversely solved by the previously obtained second-order sensitivity matrix, and finally the assembly and adjustment are guided according to the reversely solved detuning quantity.
2. The adjusting method based on the second-order sensitivity matrix method as claimed in claim 1, wherein in the first step, the off-axis reflective telescope system is a series of telescope systems with an entrance pupil deviating from a main optical axis, but not limited to the off-axis reflective telescope system, and can be an on-axis refractive telescope system.
3. The method according to claim 1, wherein the second step is a step of adjusting the primary and secondary mirrors by an off-axis amount d in the directions of the horizontal and vertical axesm x dm yThe displacement of the secondary mirror relative to the primary mirror position in the X-axis and y-axis directions deviating from the primary axis is respectively, the direction of the secondary mirror is based on the direction of a Cartesian coordinate system, and the Cartesian coordinate system is set as follows: the optical axis is the Z axis, and the light propagation direction is positive; the Y axis and the Z axis form a meridian plane, and the upward direction is the positive direction of the Y axis; the X axis and the Z axis form a sagittal plane, and the outward direction is the positive direction of the X axis; amount of inclination tm x tm yThe angles of rotation of the secondary mirror about the X-axis and about the Y-axis, respectively, with respect to the primary mirror.
4. The method according to claim 1, wherein the Zernike coefficients in step two are set up by a second-order sensitivity matrix methodThe method comprises the following steps: w (ρ, θ) ═ A0+A1*ρcosθ+A2*ρsinθ+A3*(2ρ2-1)+A4*ρ2cos2θ+A5*ρ2sin2θ+A6*(3ρ2-2)ρcosθ+A7*(3ρ2-2) ρ sin θ, A in the formula0，A1，A2，A3，A4，A5，A6，A7I.e. the first eight zernike coefficients.
5. The adjusting method based on the second-order sensitivity matrix method of claim 4, wherein the first eight Zernike coefficients in steps two, five and the first ten are not limited to the first eight, but may be the first nine, the first ten, etc. terms that can accurately represent the first n (n-8, 9, 10.) Zernike coefficients of the wavefront aberration.
6. The tuning method according to claim 1, wherein the zernike coefficient difference in step three is a difference between a wave aberration with an alignment error and a system intrinsic wave aberration, and represents an amount of change in the system wave aberration caused by the misalignment.
7. The adjusting method based on the second-order sensitivity matrix method of claim 1, wherein the corresponding relationship between the zernike coefficients and the aberrations in step four can be a one-to-one mapping relationship between the zernike coefficients and the system wavefront aberrations, such as the first term representing the optical path difference, the second three terms representing the tilt amount, the fourth term representing the defocus amount, the fifth six terms representing the astigmatism, and the seventh eight terms representing the coma aberration.
8. The method of claim 1, wherein the least squares fitting is based on N sets of Zernike coefficient differences Δ Zm nAnd correspondingly four d1 x d1 y t1 x t1 yLeast squares for the amount of detuningThe method performs a fitting of a multi-order function to the Zernike coefficients and the amount of alignment misregistration.
9. The method of claim 1 wherein the wavefront sensor of step six is an optical sensor device that converts systematic wavefront aberrations into those characterized by zernike polynomials.
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