CN112946880A - Model-based automatic adjustment method for wavefront-free sensor optical system - Google Patents
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Abstract
The invention relates to a model-based automatic adjustment method for an optical system without a wavefront sensor, which solves the technical problems and defects that the existing automatic adjustment technology for the optical system needs an additional wavefront sensor, is low in convergence speed, is easy to fall into a local extreme value and the like, and belongs to the technical field of optics. The method applies the model-based wavefront-free sensor adaptive optics technology to the adjustment of the optical system, directly solves the misalignment amount of the system by utilizing the linear relation between the image evaluation function and the degree of freedom of the detuning mirror, does not need an additional wavefront sensor, and has high adjustment speed and high accuracy.
Description
Technical Field
The invention relates to a model-based automatic adjusting method for an optical system of a wavefront-free sensor, and belongs to the technical field of optics.
Background
With the development of modern optics, the requirements of people on imaging quality are continuously increased, and the structure of an optical system is increasingly complicated. This not only increases the difficulty for the design and processing of the optical system, but also increases the requirements for the installation and adjustment of the optical system. The imaging quality of the optical system is directly affected by the correctness of the relative position of the optical elements in the system.
Generally, the installation and adjustment of the optical system are mainly performed by the experience of the installation and adjustment personnel and the interferometer, and the installation and adjustment personnel adjusts the position of the optical element by the experience of the interference pattern obtained by the interferometer so as to enable the interference pattern to meet the expected requirement. Obviously, the method needs experienced assembly personnel, has long assembly period and poor accuracy, and is difficult to apply under certain special environments (such as space orbit). Therefore, it is necessary to develop a high-precision automatic adjustment method for an optical system.
The traditional automatic adjustment method of the optical system is mainly divided into two types: one is a fitting method based on wavefront error detection, and the other is a fitting method based on image evaluation function iterative optimization. The adjustment method based on the wave-front error detection comprises two steps of wave-front detection and maladjustment correction, wherein a shack-Hartmann wave-front sensor, an interferometer and the like can be used for the wave-front detection; the maladjustment correction method comprises a sensitivity matrix inversion method, an evaluation function regression method, a vector aberration theory method and the like. This type of tuning method requires additional detection equipment, increasing the complexity and cost of the system. The image evaluation function iterative optimization-based debugging method generally takes image sharpness as an evaluation function, adopts a certain optimization algorithm to make the evaluation function converge to an extreme value, and the optimization algorithm comprises a genetic algorithm, a simulated annealing algorithm or a random parallel gradient descent algorithm and the like. Although no additional device is needed in the debugging method, the algorithm has slow convergence speed and is easy to fall into local extreme values.
Disclosure of Invention
The invention aims to solve the technical problems and defects that an existing optical system automatic adjusting technology needs an additional wavefront sensor, is low in convergence speed and easy to fall into a local extreme value and the like, and provides a novel model-based wavefront-sensor-free optical system automatic adjusting method.
The method has the innovation points that: the method comprises the steps of obtaining an influence function of each degree of freedom of a to-be-adjusted mirror by using optical design software, solving a response matrix, acquiring n +1 image estimation correction parameters and calculating an evaluation function by introducing n times of to-be-adjusted mirror offset, solving a misalignment amount, and adjusting the to-be-adjusted mirror to achieve the purposes of correcting aberration and improving image quality.
A model-based automatic adjustment method for an optical system of a wavefront-free sensor comprises the following steps:
step 1: and determining an influence function of the degree of freedom of the system to be adjusted.
The method comprises the following specific steps:
an optical element in an optical system may have misalignment in multiple degrees of freedom of movement, including translation in the X/Y/Z direction and rotation in the X/Y/Z direction. Therefore, it is necessary to determine the effect of each of the degrees of freedom that may produce misalignment on the phase distribution of the exit pupil wavefront.
When the optical system is designed, the design value phi of the exit pupil wavefront is obtained by using optical design software (such as ZEMAX, CODE V, etc.)0. Applying a unit shift amount to the ith to-be-adjusted degree of freedom of the optical system, and obtaining the exit pupil wavefront phi after applying the shift amount by using optical design softwarei. Definition FiThe expression of the impact function of the ith degree of freedom to be adjusted is as follows:
Fi＝φi-φ0 (1)
and n is the sum of the degrees of freedom of all optical elements to be adjusted.
And after obtaining the influence function of the ith to-be-installed and adjusted degree of freedom, restoring the ith to-be-installed and adjusted degree of freedom, and obtaining the influence functions of the rest to-be-installed and adjusted degrees of freedom according to the same steps until obtaining the influence functions of the n degrees of freedom.
The total exit pupil wavefront error φ caused by the optical system misalignment is expressed as:
wherein, aiAnd the misadjustment amount of the ith to-be-adjusted degree of freedom is obtained.
Step 2: and acquiring a response matrix of the optical system to be adjusted.
The method comprises the following specific steps:
calculating the gradient of the influence function of each degree of freedom to be adjusted and calculating the inner product alpha between every twokl：
Wherein, Fk、FlRespectively representing the influence functions of the kth and the l to-be-adjusted degrees of freedom of the optical system, wherein k is 1: n, and l is 1: n;
representing the gradient operator and P the pupil area. dA represents the differential of the area.
Response matrix Q of optical system is defined by alphaklThe composition is expressed as:
and step 3: an initial evaluation function of the detuning system is calculated and correction parameters are estimated.
The method comprises the following specific steps:
acquiring an image I when the optical system is in the initial misalignment positioneCalculating the inverse of the integral of the image power spectral density in the low frequency space as an initial evaluation function ge：
Wherein S ise(m, xi) is image IeThe power spectral density (M, xi) is a polar coordinate of a frequency domain, M1And M2Is a preset value in the frequency domain that is less than the cutoff frequency of the detector that acquired the image.
According to image IePower spectral density S ofe(m, ξ), estimating correction parameters
Wherein H0(m, ξ) is the normalized optical transfer function for the diffraction limit case.
And 4, step 4: positive biases are applied n times in sequence and an evaluation function is calculated.
The method comprises the following specific steps:
and sequentially introducing positive offset to each degree of freedom to be adjusted, wherein the offset is b. Respectively collecting the images I with the introduction of the biasiObtaining an evaluation function g of the imagei：
Wherein S isi(m, xi) is image IiI-1: n.
And 5: and calculating the detuning amount of the degree of freedom to be debugged.
The method comprises the following specific steps:
the relation between the detuning amount of the degree of freedom to be debugged and the evaluation function is as follows:
wherein T represents a matrix transpose; geIs an initial evaluation function; gamma is a gain factor, preferably, gamma epsilon [1.2,1.4] is taken]。
The detuning amount a of the degree of freedom to be debugged is as follows:
wherein the content of the first and second substances,
representing the matrix inversion.
Step 6: and correcting the freedom degree to be adjusted.
a contains all the detuning amount of the degree of freedom to be adjusted, and treatsAdjustment degree of freedom application-aiThe offset can be corrected by the correction amount of (2).
And 7: and judging whether the image after being adjusted meets the quality requirement. And if the requirements are not met, returning to the step 3. And if the requirements are met, finishing the debugging process.
Advantageous effects
Compared with the existing automatic optical system adjusting method, the method of the invention has the following advantages:
the method applies the model-based wavefront-free sensor adaptive optics technology to the adjustment of the optical system, directly solves the misalignment amount of the system by utilizing the linear relation between the image evaluation function and the degree of freedom of the detuning mirror, does not need an additional wavefront sensor, and has high adjustment speed and high accuracy.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a schematic view of an optical system of the method of the present invention;
FIG. 3 is a schematic diagram of the impact function of the method of the present invention;
FIG. 4 is a diagram illustrating simulation results of the method of the present invention.
Detailed Description
The method of the present invention will be described in further detail with reference to the accompanying drawings and examples.
Examples
In order to verify the feasibility of the method of the invention, an optical system as shown in fig. 2 was chosen for the simulated tuning in combination with the optical design software ZEMAX. In the simulation system, taking the secondary mirror in the maladjustment state and taking the other mirrors in the standard positions as examples, the adjustment process of the secondary mirror with the central view field of the secondary mirror with the Z-direction translation, the X-direction translation, the Y-direction translation, the X-direction rotation and the Y-direction rotation with 5 degrees of freedom (n is 5) is given.
As shown in fig. 1, a model-based wavefront-free sensor optical system automatic tuning method includes the following steps:
step 1: and determining an influence function of the degree of freedom of the system to be adjusted.
The method comprises the following specific steps:
in the optical design of softThe optical system shown in FIG. 2 was turned on in element ZEMAX to record the design state central field exit pupil wavefront φ0. Applying a unit shift amount (for example, the Z direction translation is 1 μm, the X direction translation is 10 μm, the Y direction translation is 10 μm, the X direction rotation is 1.44arcsec, and the Y direction rotation is 1.44arcsec) to the i-th to-be-adjusted degree of freedom of the secondary mirror, and obtaining the exit pupil wavefront phi after applying the shift amount by using optical design softwarei. Definition FiThe expression of the impact function of the ith degree of freedom to be adjusted is as follows:
Fi＝φi-φ0 (1)
wherein, i is 1: n, and n is 5.
After obtaining the influence function of the ith to-be-adjusted degree of freedom, restoring the ith to-be-adjusted degree of freedom, and obtaining the influence functions of the remaining to-be-adjusted degrees of freedom according to the same steps until obtaining the influence functions of the 5 degrees of freedom of the secondary mirror, as shown in fig. 3.
The total exit pupil wavefront error φ caused by the optical system misalignment is expressed as:
wherein, aiAnd the misadjustment amount of the ith to-be-adjusted degree of freedom is obtained.
Step 2: and acquiring a response matrix of the optical system to be adjusted.
The method comprises the following specific steps:
calculating the gradient of the influence function of each degree of freedom to be adjusted and calculating the inner product alpha between every twokl：
Wherein, Fk、FlRespectively representing the influence functions of the kth and the l to-be-adjusted degrees of freedom of the optical system, wherein k is 1: n, and l is 1: n;
representing the gradient operator and P the pupil area. dA represents the differential of the area.
Response matrix Q of optical system is defined by alphaklThe composition is expressed as:
and step 3: an initial evaluation function of the detuning system is calculated and correction parameters are estimated.
The method comprises the following specific steps:
applying a random detuning quantity to the secondary mirror in the optical design software to acquire an image IeCalculating the inverse of the integral of the image power spectral density in the low frequency space as an initial evaluation function ge：
Wherein S ise(m, xi) is image IeThe power spectral density (M, xi) is a polar coordinate of a frequency domain, M1＝1/128，M2＝6/128。
According to image IePower spectral density S ofe(m, ξ), estimating correction parameters
Wherein H0(m, ξ) is the normalized optical transfer function for the diffraction limit case.
And 4, step 4: positive biases are applied n times in sequence and an evaluation function is calculated.
The method comprises the following specific steps:
and sequentially introducing positive offset to each degree of freedom to be adjusted of the secondary mirror, wherein the offset is b (b is 1, namely a unit movement amount). Separately collecting incoming offsetsLater image IiObtaining an evaluation function g of the imagei：
Wherein S isi(m, xi) is image IiI-1: n.
And 5: and calculating the detuning amount of the degree of freedom to be debugged.
The method comprises the following specific steps:
the relationship between the detuning amount of the degree of freedom of the secondary mirror to be adjusted and the evaluation function is as follows:
wherein T represents a matrix transpose; geIs an initial evaluation function; γ is a gain factor, and in this embodiment, γ is 1.3.
The detuning amount a of the degree of freedom to be debugged is as follows:
wherein the content of the first and second substances,
representing the matrix inversion.
Step 6: and correcting the freedom degree to be adjusted.
a contains the detuning amount of 5 to-be-adjusted degrees of freedom of the secondary mirror, and applies-a to the to-be-adjusted degrees of freedomiThe offset can be corrected by the correction amount of (2).
And 7: and judging whether the image after being adjusted meets the quality requirement. And if the requirements are not met, returning to the step 3. And if the requirements are met, finishing the debugging process.
The final adjustment result is shown in fig. 4, which respectively shows the ideal state, the detuning state and the adjusted imaging result of the optical system.
Claims (3)
1. A model-based automatic adjustment method for an optical system of a wavefront-free sensor is characterized by comprising the following steps:
step 1: determining an influence function of the degree of freedom of a system to be adjusted;
after the optical system is designed, the design value phi of the exit pupil wavefront is obtained by using optical design software0；
Applying a unit shift amount to the ith to-be-adjusted degree of freedom of the optical system, and obtaining the exit pupil wavefront phi after applying the shift amount by using optical design softwarei(ii) a Definition FiThe expression of the impact function of the ith degree of freedom to be adjusted is as follows:
Fi＝φi-φ0 (1)
n is the sum of the degrees of freedom of all optical elements to be adjusted;
after obtaining the influence function of the ith to-be-installed and adjusted degree of freedom, restoring the ith to-be-installed and adjusted degree of freedom, and obtaining the influence functions of the rest to-be-installed and adjusted degrees of freedom according to the same steps until obtaining the influence functions of the n degrees of freedom;
the total exit pupil wavefront error φ caused by the optical system misalignment is expressed as:
wherein, aiThe misadjustment quantity of the ith to-be-adjusted degree of freedom is taken as the misadjustment quantity of the ith to-be-adjusted degree of freedom;
step 2: acquiring a response matrix of an optical system to be adjusted;
calculating the gradient of the influence function of each degree of freedom to be adjusted and calculating the distance between every twoInner product of alphakl：
Wherein, Fk、FlRespectively representing the influence functions of the kth and the l to-be-adjusted degrees of freedom of the optical system, wherein k is 1: n, and l is 1: n;
represents the gradient operator, P the pupil area, dA the differential of the area;
response matrix Q of optical system is defined by alphaklThe composition is expressed as:
and step 3: calculating an initial evaluation function of the maladjustment system, and estimating a correction parameter;
acquiring an image I when the optical system is in the initial misalignment positioneCalculating the inverse of the integral of the image power spectral density in the low frequency space as an initial evaluation function ge：
Wherein S ise(m, xi) is image IeThe power spectral density (M, xi) is a polar coordinate of a frequency domain, M1And M2Is a preset value in the frequency domain that is less than the cutoff frequency of the detector that collects the image;
according to image IePower spectral density S ofe(m, ξ), estimating correction parameters
Wherein H0(m, ξ) is the normalized optical transfer function for the case of diffraction limits;
and 4, step 4: sequentially applying n times of positive bias and calculating an evaluation function;
sequentially introducing positive bias to each degree of freedom to be assembled and adjusted, wherein the bias is b; respectively collecting the images I with the introduction of the biasiObtaining an evaluation function g of the imagei：
Wherein S isi(m, xi) is image IiI is 1: n;
and 5: calculating the detuning amount of the degree of freedom to be installed and debugged;
the relation between the detuning amount of the degree of freedom to be debugged and the evaluation function is as follows:
wherein T represents a matrix transpose; geIs an initial evaluation function; gamma is a gain factor;
the detuning amount a of the degree of freedom to be debugged is as follows:
wherein the content of the first and second substances,
representing the matrix inversion.
Step 6: correcting the freedom degree of the to-be-installed adjustment;
and 7: and (3) judging whether the image after installation and debugging meets the quality requirement, if not, returning to the step (3), and if so, ending the installation and debugging process.
2. The method for automatically tuning a model-based wavefront-free sensor optical system of claim 1 wherein in step 5 γ e [1.2,1.4 ].
3. The method according to claim 1, wherein in the step 6, a includes all the misalignment amounts of the degrees of freedom to be adjusted, and-a is applied to the degrees of freedom to be adjustediThe offset can be corrected by the correction amount of (2).
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