CN103175611B - Free-form optical device used for correcting astigmatism and coma aberration in spectrograph - Google Patents

Abstract

The invention relates to the improvement of the spectrometer and aims to provide a free-form surface optical device for correcting the astigmatism and coma of the spectrometer. The spectrometer includes a light source, an incident slit, a concave collimating mirror, a plane diffraction grating, a concave imaging mirror and a photodetector. The free-form optical device is located between the concave imaging mirror and the photodetector. The upper surface of the free-form optical device is free The curved surface, the lower surface is a plane, and the lower surface is stacked with photodetectors. The present invention is arranged on the photodetector (linear CCD array) of the spectrometer, and the curvature of the freeform surface on the upper surface of the present invention changes along the direction of dispersion and perpendicular to the direction of dispersion respectively, respectively correcting the meridional coma and astigmatism of the spectrometer, improving the collection Light efficiency increases the sensitivity of the spectrometer.

Description

Freeform Optics for Correcting Spectrometer Astigmatism and Coma

technical field

The invention relates to the improvement of the spectrometer, in particular to a free-form surface optical device for simultaneously correcting the meridional coma and astigmatism in the wide band of the spectrometer system.

Background technique

Spectroscopic instruments are generally used to determine the spectral composition of light sources, including spectral wavelength distribution, intensity response, and spectral bandwidth. Taking the traditional Czerny-Turner spectrometer as an example, it includes an incident slit, a plane diffraction grating, a collimating mirror, an imaging mirror, and a photodetector. The collimating mirror collimates the incident beam and reflects it to the diffraction grating, and the mirror focuses the beam dispersed by the diffraction grating onto the detector. The commonly used photodetector is a linear CCD array, so it is necessary to improve the light collection efficiency of the spectrometer and resolution.

In the Czerny-Turner spectrometer system, the light passes through the off-axis collimating mirror and imaging mirror, the optical path to the image plane is different, and the intersection point with the chief ray is different, so aberration occurs. In the meridian plane, the marginal rays on both sides are reflected by the mirror and intersect with the chief ray at different points, thus producing meridional coma. At the same time, after the light is reflected by the reflection system, the intersection point of the beam in the meridian plane and the chief ray and the intersection point of the beam in the sagittal plane and the chief ray do not coincide, so astigmatism is obtained. Astigmatism and coma are the main factors affecting the light collection efficiency and resolution of the CCD array, so these two types of aberrations need to be corrected in the spectrometer.

A common method is to add a cylindrical mirror on the image plane of the spectrometer, but the cylindrical mirror can only correct the astigmatism of the spectrometer. The method of correcting the coma of the spectrometer system: adjust the parameters of the optical system, that is, select the appropriate off-axis angle and radius of curvature of the collimating mirror, the off-axis angle and radius of curvature of the imaging mirror, and the incident angle and diffraction angle of the light on the grating, so that These parameters satisfy the Shafer formula to correct the coma at a specific wavelength. However, this method can only correct the coma at the central wavelength, and the coma of the entire optical system is distributed in a V shape as the wavelength changes.

In order to obtain the maximum resolution and light collection efficiency of the spectrometer, an optical device is required to simultaneously correct the astigmatism and broadband meridional coma of the spectrometer.

Contents of the invention

The main purpose of the present invention is to overcome the deficiencies in the prior art, and provide a free-form surface optical device capable of simultaneously correcting the meridional coma and astigmatism in the wide band of the existing spectrometer. In order to solve the problems of the technologies described above, the solution of the present invention is:

A free-form surface optical device for correcting astigmatism and coma of a spectrometer is provided, the spectrometer includes a light source, an incident slit, a concave collimator mirror, a plane diffraction grating, a concave imaging mirror and a photodetector, wherein the free-form surface The curved optical device is located between the concave imaging mirror and the photodetector, the upper surface of the free-form optical device is a free-form surface, the lower surface is a plane, and the lower surface is stacked with the photodetector; the free-form surface is determined by the following method:

A. Calculate the total coma generated by the beam passing through the concave collimator mirror, the plane diffraction grating and the concave imaging mirror: the light path function of the beam entering the spectrometer from the incident slit and reflected by the concave collimator mirror to the plane diffraction grating can be expressed as:

Among them, F ₁ is the optical path of the marginal ray from the incident slit to the concave collimator and then to the plane diffraction grating, r, r' are the optical paths before and after the main ray passes through the concave collimator, ω is the optical path of the marginal ray on the concave collimator The distance between the straight mirror and the chief ray, α, α' are the incident angle and exit angle of the chief ray on the concave collimator, respectively, and _R1 is the radius of curvature of the concave collimator;

Since the light behind the concave collimator is parallel light, r' = ∞;

From the geometric relationship of the beam, we can get ω=ω′/cosα′, ;

Among them, ω' is the half-width of the parallel beam passing through the concave collimating mirror, W is the width of the plane diffraction grating, and α _g is the incident angle of the parallel beam on the plane diffraction grating, so formula (1) can be simplified:

According to Fermat's principle, that is , you can get:

According to the principle of reflection, α = -α' can be obtained, and the first item of formula (2) is zero;

Pick Make the second term of formula (2) also be zero, then formula (2) can be expressed as:

can get , that is, formula (3) is the angular aberration produced by the light passing through the concave collimator, and ∂α _g represents the coma after the light passes through the concave collimator;

According to the grating equation mλ=d(sinα _g +sinβ _g ), wherein, m is an integer, λ is the wavelength, d is the grating constant, and β _g is the diffraction angle of light of this wavelength on the plane diffraction grating;

It can be obtained that the angular aberration produced by the concave collimator is diffracted by the plane diffraction grating and becomes:

Among them, ∂β _g represents the angular aberration after the light passes through the concave collimator and the plane diffraction grating, and ∂β _g represents the coma after the light passes through the plane diffraction grating;

In the same way, the coma aberration produced by light passing through the concave imaging mirror can be deduced;

Assuming that the light path function from the plane diffraction grating to the concave imaging mirror and then to the image plane is F ₂ , then the derivation process of F ₂ is consistent with the derivation process of light from the incident slit to the concave collimator to the plane diffraction grating, so :

Among them, F ₂ is the optical path of the marginal ray from the plane diffraction grating to the concave imaging mirror and then to the image plane, β is the incident angle of the chief ray on the concave imaging mirror, and R ₂ is the radius of curvature of the concave imaging mirror;

Therefore, the total coma _Δt produced by the concave collimator, the plane diffraction grating and the concave imaging mirror can be expressed as:

B. Calculate the coma aberration generated by the beam of each wavelength in the spectrometer structure after adding the free-form surface optical device: add the free-form surface optical device above the photodetector, and replace the curvature of the intersection part of the beam with the free-form surface by R ₃ , the free-form surface The refractive index of the material of the optical device corresponding to the wavelength is replaced by n,

The optical path function _F30 of the light from the plane diffraction grating to the concave imaging mirror to the free-form surface optical device and finally to the image surface can be expressed as: increasing the light from the plane diffraction grating to the concave imaging mirror to the original image surface Subtract the optical path from the position of the free-form surface to the original image surface before adding the free-form surface, and add the optical path from the position of the free-form surface to the current image surface after adding the free-form surface; F ₃₀ can be expressed as:

F ₃₀ =F ₂ +F ₃ (7)

Among them, the optical path F ₂ of the free-form front light from the plane diffraction grating to the concave imaging mirror to the original image plane has been deduced before, and the remaining optical path F ₃ can be expressed as:

Among them, _F3 represents the change of the optical path of the marginal ray from the free-form surface optical device to the image plane after the free-form surface is added, and before the free-form surface is added, _ω3 is the distance between the edge ray and the chief ray of the beam on the free-form surface optical device, r ₃ and r′ ₃ are respectively the optical path of the chief ray from this position to the image plane when the free-form surface optical device is not added and after the free-form surface optical device is added, and β ₃ and β′ ₃ are respectively the chief ray on the free-form surface optical device The angle of incidence and angle of refraction;

Calculate the partial guide of the width ω of the light beam on the concave collimator by formula (8), and according to the principle of refraction sinβ ₃ =nsinβ′ ₃ , the optical path difference can be expressed as:

Select the conditions of r ₃ , r ₃ ', R ₃ , and β ₃ to make the first item in formula (9) equal to 0, and combine the geometric relationship to obtain the relationship of formula (10):

Then the coma _Δc produced by the free-form surface can be expressed as:

To sum up, the coma Δ generated by the beam of each wavelength in the spectrometer structure after adding the free-form surface optical device is:

Δ= _Δt + _Δc (12)

C. Determine the free-form surface: use the evaluation function to minimize the sum of the meridional coma of the spectrometer within a certain band range, so as to correct the wide-band coma;

The four variables β ₃ , r ₃ , R ₃ , and n in formula (11) vary with the wavelength, and the variable values corresponding to a certain wavelength are counted as β _3λ , r _3λ , R _3λ , n _λ , where n _λ is the refractive index of the current wavelength; first take the appropriate r ₃₀ , which indicates the position of the intersection point between the principal ray of the central wavelength and the free-form surface; and it is stipulated that the radius of curvature and center of curvature of each point on the curve formed by the intersection of the free-form surface and the meridian surface can be different, but the curvature The center must be located on the straight line where the principal ray of the central wavelength is located, then for each selected R _3λ , the determined β _3λ and r _3λ can be obtained according to the geometric relationship, so the optimization process is to find the corresponding wavelength of each wavelength within a certain range R _3λ , making the evaluation function of formula (13) the smallest;

According to the optimized variable value, the intersection position and curvature of the free-form surface and the chief ray of each wavelength in the meridian plane can be determined, and these values can be fitted into a curve, which is the curve formed by the intersection of the free-form surface and the meridian plane. Then choose the appropriate curvature of the curve perpendicular to the meridian plane and intersected with the curve to correct astigmatism, that is, to determine the free-form surface we need.

In the present invention, the central thickness of the free-form surface optical device is 9.4 mm.

In the present invention, the free-form surface optical device is an optical device made of optical glass.

In the present invention, the curvature radius of the free-form surface perpendicular to the dispersion direction is between 4.5 mm and 5.5 mm.

Compared with prior art, the beneficial effect of the present invention is:

A free-form surface optical device is added to the photodetector (linear CCD array) of the spectrometer. The free-form surface curvature of the free-form surface optical device changes along the dispersion direction and the direction perpendicular to the dispersion, respectively, and the meridian coma and astigmatism of the spectrometer are respectively corrected to improve The light collection efficiency is improved, and the sensitivity of the spectrometer is increased.

Description of drawings

Fig. 1 is a structural diagram of the present invention.

Figure 2 is a cross-sectional view of the present invention.

Fig. 3 is a schematic side view of the present invention.

Fig. 4 is a schematic diagram of the lower surface of the present invention.

Fig. 5 is a system diagram of a spectrometer installed with the present invention.

Fig. 6 is a schematic diagram of a meridional direction of a free-form surface corresponding to a certain wavelength.

Fig. 7 is an optical path diagram of a concave collimating mirror in a spectrometer.

Reference signs in the figure are: 1 light source; 2 incident slit; 3 concave collimating mirror; 4 plane diffraction grating; 5 concave imaging mirror; 6 upper surface of free-form optical device; 7 lower surface of free-form optical device; 8 photodetector; 9 incident light beam; 10 collimated light beam; 11 imaging light beam.

Detailed ways

Below in conjunction with accompanying drawing and specific embodiment the present invention is described in further detail:

The spectrometer includes a light source 1, an incident slit 2, a concave collimator mirror 3, a plane diffraction grating 4, a concave imaging mirror 5, and a photodetector 8, specifically a Czerny-Turner spectrometer.

In order to correct the meridional coma aberration of the wide band of the spectrometer system, the present invention places a free-form surface optical device between the concave imaging mirror 5 and the photodetector 8 . As shown in FIG. 1 , the upper surface 6 of the free-form surface optical device is a free-form surface, and the curvature of the curved surface along the dispersion direction changes with different wavelengths intersecting it, so as to correct the meridional coma of each wavelength. In the direction perpendicular to the dispersion, the curved surface also has a certain curvature, which is used to correct the astigmatism. The lower surface 7 of the free-form surface optical device is attached to the photodetector 8, so it is plane. The central thickness of the free-form surface optical device is 9.4mm, and the curvature radius of the free-form surface perpendicular to the dispersion direction is between 4.5mm and 5.5mm. The material of the free-form surface optical device is optical glass, and common glass such as K9 can be selected.

The freeform surface is determined by the following method:

A. Calculate the total coma generated by the light beam passing through the concave collimating mirror 3, the plane diffraction grating 4 and the concave imaging mirror 5: the light beam is incident on the spectrometer from the incident slit 2, and is reflected by the concave collimating mirror 3 to the light of the plane diffraction grating 4 The program function can be expressed as:

Among them, F ₁ is the optical path of the marginal ray from the incident slit 2 to the concave collimator 3 and then to the plane diffraction grating 4, r and r' are the optical paths of the chief ray before and after passing through the concave collimator 3, ω is the edge The distance between the ray and the chief ray on the concave collimator 3, α, α' are the incident angle and the exit angle of the chief ray on the concave collimator 3 respectively, and _R1 is the radius of curvature of the concave collimator 3.

Since the light behind the concave collimator 3 is parallel light, r' = ∞;

From the geometric relationship of the beam, we can get ω=ω′/cosα′, ;

Among them, ω' is the half-width of the parallel beam passing through the concave collimator 3, W is the width of the plane diffraction grating 4, and α _g is the incident angle of the parallel beam on the plane diffraction grating 4, so formula (1) can be Do the simplification:

According to Fermat's principle, that is , you can get:

According to the principle of reflection, α = -α' can be obtained, and the first item of formula (2) is zero;

Pick Make the second term of formula (2) also be zero, then formula (2) can be expressed as:

can get , that is, formula (3) is the angular aberration generated by the light passing through the concave collimator 3, and ∂α _g represents the coma after the light passes through the concave collimator 3.

According to the grating equation mλ=d( _sinαg + _sinβg ), wherein, m is an integer, λ is a wavelength, d is a grating constant, and _βg is the diffraction angle of light of this wavelength on the plane diffraction grating 4;

It can be obtained that the angular aberration generated by the concave collimator 3 is diffracted by the plane diffraction grating 4 and becomes:

Among them, ∂β _g represents the angular aberration of the light after passing through the concave collimator 3 and the plane diffraction grating 4 , and ∂β _g represents the coma aberration of the light after passing through the plane diffraction grating 4 .

In the same way, it can be deduced that the coma generated after the light passes through the concave imaging mirror 5;

Assuming that the optical path function of the light from the plane diffraction grating 4 to the concave imaging mirror 5 and then to the image plane is _F2 , then the derivation process of _F2 is the same as that of the light from the incident slit 2 to the concave collimator 3 to the plane diffraction grating 4 The derivation process is consistent, so:

Among them, _F2 is the optical path of the marginal ray from the plane diffraction grating 4 to the concave imaging mirror 5 and then to the image plane, β is the incident angle of the chief ray on the concave imaging mirror 5, and _R2 is the radius of curvature of the concave imaging mirror 5.

Therefore, the total coma _Δt produced by the concave collimator 3, the plane diffraction grating 4 and the concave imaging mirror 5 can be expressed as:

B. Calculate the coma aberration produced by the light beam of each wavelength in the spectrometer structure after adding the free-form surface optical device: increase the free-form surface optical device above the photodetector 8, and the curvature of the intersecting part of the light beam and the free-form surface is replaced by R ₃ , free The refractive index of the material of the curved optical device corresponding to the wavelength is replaced by n.

The light from the plane diffraction grating 4 to the concave imaging mirror 5, and then to the free-form surface optical device, finally reaches the optical path function _F30 of the image plane, which can be expressed as: increasing the free-form front light from the plane diffraction grating 4 to the concave imaging mirror 5 to the original The optical path of the image surface, minus the optical path from the position of the free-form surface to the original image surface before adding the free-form surface, plus the optical path from the position of the free-form surface to the existing image surface after adding the free-form surface; F ₃₀ can be expressed as:

F ₃₀ =F ₂ +F ₃ (7)

Among them, the optical path F2 of the free-form front light from the plane diffraction grating 4 to the concave imaging mirror ₅ to the original image plane has been deduced before, and the remaining optical path _F3 can be expressed as:

Among them, _F3 represents the change of the optical path of the marginal ray from the free-form surface optical device to the image plane after the free-form surface is added, and before the free-form surface is added, _ω3 is the distance between the edge ray and the chief ray of the beam on the free-form surface optical device, r ₃ and r′ ₃ are respectively the optical path of the chief ray from this position to the image plane when the free-form surface optical device is not added and after the free-form surface optical device is added, and β ₃ and β′ ₃ are respectively the chief ray on the free-form surface optical device angle of incidence and angle of refraction.

Calculate the deflection of the beam width ω on the concave collimating mirror 3 by formula (8), and according to the principle of refraction sinβ ₃ =nsinβ′ ₃ , the optical path difference can be expressed as:

Select the conditions of r ₃ , r ₃ ', R ₃ , and β ₃ to make the first item in formula (9) equal to 0, and combine the geometric relationship to obtain the relationship of formula (10):

Then the coma _Δc produced by the free-form surface can be expressed as:

To sum up, the coma Δ generated by the beam of each wavelength in the spectrometer structure after adding the free-form surface optical device is:

Δ= _Δt + _Δc (12)

C. Determine the free-form surface: use the evaluation function to minimize the sum of the meridional coma of the spectrometer within a certain band range, so as to correct the wide-band coma;

The four variables β ₃ , r ₃ , R ₃ , and n in formula (11) vary with the wavelength, and the variable values corresponding to a certain wavelength are counted as β _3λ , r _3λ , R _3λ , n _λ , where n _λ is the refractive index of the current wavelength; first take the appropriate r ₃₀ , which indicates the position of the intersection point between the principal ray of the central wavelength and the free-form surface; and it is stipulated that the radius of curvature and center of curvature of each point on the curve formed by the intersection of the free-form surface and the meridian surface can be different, but the curvature The center must be located on the straight line where the principal ray of the central wavelength is located, then for each selected R _3λ , the determined β _3λ and r _3λ can be obtained according to the geometric relationship, so the optimization process is to find the corresponding wavelength of each wavelength within a certain range R _3λ , making the evaluation function of formula (13) the smallest.

According to the optimized variable value, the intersection position and curvature of the free-form surface and the chief ray of each wavelength in the meridian plane can be determined, and these values can be fitted into a curve, which is the curve formed by the intersection of the free-form surface and the meridian plane. Then choose the appropriate curvature of the curve perpendicular to the meridian plane and intersected with the curve to correct astigmatism, that is, to determine the free-form surface we need.

The free-form surface optical device made of the determined free-form surface on the upper surface is arranged on the photodetector 8, which can be used to simultaneously correct the meridional coma and astigmatism in the wide band of the existing spectrometer.

Claims (4)

1. A free-form surface optical device for correcting astigmatism and coma aberration of a spectrograph comprises a light source, an incident slit, a concave collimating mirror, a planar diffraction grating, a concave imaging mirror and a photoelectric detector, and is characterized in that the free-form surface optical device is positioned between the concave imaging mirror and the photoelectric detector, the upper surface of the free-form surface optical device is a free-form surface, the lower surface of the free-form surface optical device is a plane, and the lower surface of the free-form surface optical device is overlapped with the photoelectric detector; the free-form surface is determined by the following method:

A. and calculating the total coma generated by the light beam passing through the concave collimating mirror, the plane diffraction grating and the concave imaging mirror: the optical path function of a light beam entering the spectrometer from the entrance slit and reflected to the planar diffraction grating by the concave collimator can be expressed as:

wherein,the light path of the marginal ray from the entrance slit to the concave collimating mirror and then to the planar diffraction gratingRepresenting the optical path of the light from the point where it begins to diverge to the concave collimating mirror,representing the optical path of the light from the concave collimating mirror to the light converging point;the distance between the marginal ray and the principal ray on the concave collimating mirror,the incident angle and the exit angle of the chief ray on the concave collimating mirror respectively,the radius of curvature of the concave collimating mirror;

because the light rays are emitted from the slit and become parallel light after passing through the concave collimating lens, namely, the parallel light is converged at infinity, the light rays are emitted from the slit and become parallel light after passing through the concave collimating lens, and therefore, the light rays are emitted from the slit and become parallel light after passing through the concave collimating lensIs a finite number, and

from the geometrical relationship of the beams

Wherein,is the half width of the parallel light beam after passing through the concave collimating mirror,the width of the plane diffraction grating is related to the beam width or cone angle of the light when the light propagates in the spectrometer, and the beam width or cone angle influences the aberration; the width of the grating refers to the width capable of passing light;the incident angle of the parallel light beam on the grating;

thus, equation (1) can be simplified:

according to the Fermat principle, the light path is extreme from one point to another, so that the light reaches the receiving surface from the point of emission, if this is sufficientThere is no aberration; i.e. here looking forThe conditions of (1):

according to the principle of reflection, can obtainThe first term of formula (2) is zero;

getSuch that the second term of equation (2) is also zero, equation (2) can be expressed as:

can obtainThat is, the formula (3) is the angular aberration generated by the light passing through the concave collimating mirrorExpressing coma after light passes through the concave collimating mirror;

according to the grating equationWherein,is an integer which is the number of the whole,is a function of the wavelength of the light,is a constant of the grating, and is,the diffraction angle of the wavelength light on the grating;

the angle aberration generated by the concave collimating mirror can be changed into the following by diffraction of the plane diffraction grating:

wherein,the optical system represents the angular aberration of light after passing through the concave collimating mirror and the planar diffraction grating, the angular aberration is in proportional relation with the coma aberration, and the coma aberration is reduced along with the angular aberration; so can useTo express the amount of coma after the light passes through the plane diffraction grating;

in the same way, the coma quantity generated after the light passes through the concave imaging mirror can be deduced;

the optical path function of the light from the grating to the concave imaging lens and then to the image plane is set asThe light ray refers to any light ray in the light beam, including marginal light rays; thenThe derivation process of (2) is consistent with the derivation process of light from the slit to the concave collimating mirror to the grating, so that:

wherein,the incident angle of the chief ray on the concave imaging mirror,is the radius of curvature of the concave imaging mirror;

so that the total coma generated by the concave collimating mirror, the planar diffraction grating and the concave imaging mirrorCan be expressed as:

B. calculating out coma aberration generated in the spectrometer structure by each wavelength of light beam after adding the free-form surface optical device: adding free-form surface optical device above the photoelectric detector, and using the curvature of the intersection part of the light beam and the free-form surfaceInstead, the material of the free-form surface optic has a refractive index corresponding to the wavelengthInstead of this, the user can,

the light path function from the plane diffraction grating to the concave imaging lens and then to the free-form surface optical device to the image planeCan be expressed as: increasing the optical path from the plane diffraction grating to the concave imaging mirror to the original image surface of the front light of the free-form surface, subtracting the optical path from the position of the front free-form surface of the free-form surface to the original image surface, and adding the optical path from the position of the rear free-form surface of the free-form surface to the current image surface;can be expressed as:

wherein the optical path of the light in front of the free curved surface from the plane grating to the concave imaging mirror to the original image surface is increasedThe remaining part of the optical path, which has been deduced beforeCan be expressed as:

wherein,the change of the optical path of the marginal ray from the free-form surface optical device to the image surface after the free-form surface is added and before the free-form surface is added is shown,the distance of the marginal ray of the beam from the chief ray on the free-form optical device,andthe optical paths from the position to the image plane of the chief ray are respectively when the free-form surface optical device is not added and after the free-form surface optical device is added,andthe incident angle and the refraction angle of the chief ray on the free-form surface optical device are respectively;

since the optical system is based on the law of refraction,and deriving from the geometric relationship:

thereby finishing to obtainIn relation to (2)；

Is substituted by formula (8) andto pairCalculating the partial derivatives, the optical path difference can be expressed as:

selectingWith the proviso that the first term in equation (9) is 0, and combining the geometric relationship, the relationship of equation (10) is obtained:

coma generated by the free curved surfaceCan be expressed as:

in summary, the coma aberration Δ generated in the spectrometer structure by the light beam with each wavelength after the free-form surface optical device is added is:

C. determining a free-form surface: the sum of the meridional coma aberrations of the spectrometer in a certain waveband range is reduced to the minimum by utilizing an evaluation function so as to correct the coma aberration of a wide waveband;

in the formula (11)The four variables are varied with the wavelength, and the variable value corresponding to a certain wavelength is calculated asWherein,a refractive index at the current wavelength; get the right firstThe intersection point position of the central wavelength principal ray and the free-form surface is shown; and that the radius and centre of curvature of each point on the curve formed by the intersection of the free-form surface with the meridian plane may be different, but the centre of curvature must lie on the line on which the central wavelength principal ray lies, then for each selected pointDetermined by geometric relationshipsAndso the optimization process is to find the corresponding wavelength in a certain rangeMinimizing the merit function of equation (13);

the intersection point position and curvature of the free-form surface and the principal ray of each wavelength in the meridian plane can be determined according to the optimized variable values, the values are fitted into a curve, the curve is formed by the intersection of the free-form surface and the meridian plane, and the curvature of the curve which is perpendicular to the meridian plane and intersects with the curve is selected to correct astigmatism, namely the free-form surface required by people is determined.

2. The free-form optical device of claim 1, wherein the free-form optical device has a center thickness of 9.4 mm.

3. The free-form optical device of claim 1, wherein the free-form optical device is an optical device made of optical glass.

4. The free-form optical device of claim 1, wherein a radius of curvature of the free-form surface perpendicular to the dispersion direction is between 4.5mm and 5.5 mm.