CN102253489B - Unit-magnification multi- optical path astigmatism compensation method and system thereof - Google Patents

Abstract

The invention provides a unit magnification multi-pass system optical path astigmatism compensation method and a system thereof, and belongs to the field of astigmatism compensation of a unit magnification multi-pass system. The method is characterized in that: a compensation spherical mirror is introduced behind an output aperture of a UMS (unit magnification multi-pass system) optical path which at least comprises a White optical path, various improved White optical paths and an MMS (multi-pass matrix system) optical path, the compensation spherical mirror and the whole astigmatism of the UMS optical path are compensated by adjusting the radium of the compensation mirror and the beam full divergence angle adjustment parameters, the output beam of the UMS optical path is reflected on the compensation spherical mirror, the transmission meridian plane of the compensation spherical mirror is possibly superposed with the sagittal plane of the output beam of the UMS optical path, and the astigmatism of the compensation spherical mirror is the same as that of the output beam of the UMS optical path with opposite directions, so that the astigmatism is compensated, and the divergence angle of the output beam can be further adjusted to match with the numerical aperture of a subsequent optical path.

Description

Unit many optical-path light-paths of enlargement ratio astigmatic compensation method and system thereof

Technical field

The invention belongs to the many optical-path light-paths of a kind of unit enlargement ratio (UMS light path; Unit-magnification Multi-pass System) follow-up astigmatic compensation light channel structure; This light channel structure has the astigmatic compensation function; Be applicable to the astigmatic compensation of the many optical-path light-paths of unit enlargement ratio in the optical detection system, be particularly useful for the optics cavity of field of gas detection.

Background technology

All can use the big ordinary light source of beam divergence angle in White's light path (White light path), modified White light path (modified White light path), many light paths matrix system (the MMS:Multipass Matrix System) light path; These three types of first-selections that light path is many light paths absorption spectroscopy system have been widely used in the system that trace gas detects.These light paths have same characteristics: mainly be made up of the spherical mirror of equal curvatures radius R; Catoptron in the light path can be divided into object lens and field lens; And object lens all are to be formed by the adjacent discharging of spherical mirror, and field lens then is to be separated by with object lens to be about R and to put in opposite directions, and the input aperture is placed on field lens one side with the output aperture; Therefore import the aperture by all pictures that object lens became all at the near surface of field lens, magnification is about 1: 1.Light path with this characteristics can be called the many optical-path light-paths of unit enlargement ratio (UMS light path, Unit-magnification Multi-pass System).

Field lens, the object lens front view of the structure of UMS light path and part UMS light path are as shown in Figure 1.Wherein, EA _InBe input aperture, EA _OutBe the output aperture; C _i(i=1,2,3) are object lens M _iThe center of curvature; The black point is the one-tenth image patch in input aperture; FT is the field lens of T shape bore, and FR is the field lens of rectangle bore, and FP is corner cube mirror or prism.Shown in Fig. 1, Fig. 1-the 1st, the object lens of UMS light path and the putting position of field lens.Fig. 1-2-1 object lens and Fig. 1-3-1 field lens constitutes a kind of White light path--BHWC light path (Bernstein-Herzberg White Cell; Propose by Bernstein and Herzberg; The input and output aperture is positioned over the center of curvature plane homonymy of object lens and field lens; And cut into T-shape to field lens), shown in Fig. 2-1; Fig. 1-2-1 object lens and Fig. 1-3-2 field lens constitutes another kind of White light path--PBWC light path (Pickett-Bradley WhiteCell; Propose by Pickett and Bradley; The input and output aperture is placed on the both sides on center of curvature plane respectively; The field aperture of mirror then is the rectangular shape of rule), shown in Fig. 2-2; Fig. 1-2-1 object lens and Fig. 1-3-3 field lens constitutes modified White light path, shown in Fig. 2-3; It shown in Fig. 2-4 another kind of modified White light path; Fig. 1-2-2 object lens and Fig. 1-3-4 field lens constitutes the MMS light path, shown in Fig. 2-5.

In common UMS light path, most important aberration is spherical aberration, coma and the astigmatism that makes the output facula disperse.With the spherical reflector is relatively these three kinds of aberrations of example; Like Fig. 3; Object point is P; Y is an object height, and i is an incidence angle, and i ' is an angle of reflection; U; U ' is respectively object space angular aperture and picture side's angular aperture, and R is the spherical mirror radius, and l is the object space intercept; H is that the light rise is (according to the definition of symbolic rule in the geometric optics; Along axis segment such as R, l, the direction of propagation of regulation light is positive direction from left to right; With reflecting surface summit O is initial point; By the intersection point A of summit to light to optical axis, the direction of A ' or centre of sphere C is identical with the light direction of propagation just gets, and gets negative when opposite; Vertical axis segment like light rise h, is a benchmark with the optical axis, above optical axis, for just, is negative below optical axis; The angle of light and optical axis, like u, u '; Use by optical axis and turn to the formed acute angle tolerance of light, clockwise for just, counterclockwise for negative; Therefore u in scheming; U ' is negative, and the angle of light and normal by light with acute angle directional steering normal does; Clockwise for just; Counterclockwise for negative, therefore i is for negative among the figure, and i ' is for just).When the center of curvature C of object point P skew spherical mirror, consider three rank aberrations (primary aberration), first, second, third plug Dare coefficient (Seidel coefficient, the Seidel aberration is meant primary aberration, is respectively spherical aberration, coma, astigmatism, the curvature of field, distortion) is approximate to be had:

$\mathrm{\Σ}{S}_I=\mathrm{\Σl}\·u\·n\·i\·(i-i^{\′})(i^{\′}-u)\≈2\frac{h^4}{R^3}{\left(\frac{\mathrm{\Δz}}{R}\right)}^2$

$\mathrm{\&Sigma;}{S}_{\mathrm{II}}=\mathrm{\&Sigma;}{S}_I\frac{i_p}{i}=-2\frac{{\mathrm{yh}}^3}{{\mathrm{<figure-callout\; id="3"\; label="R"\; filenames="HSA00000506963600021.png,HSA00000506963600061.png"\; state="\{\{state\}\}">R</figure-callout>}}^3}\frac{\mathrm{\&Delta;z}}{R}$

$\mathrm{\&Sigma;}{S}_{\mathrm{III}}=\mathrm{\&Sigma;}{S}_I{\left(\frac{i_p}{i}\right)}^2=2\frac{y^2{h}^2}{{\mathrm{<figure-callout\; id="3"\; label="R"\; filenames="HSA00000506963600021.png,HSA00000506963600061.png"\; state="\{\{state\}\}">R</figure-callout>}}^3}$

Their corresponding successively spherical aberration, coma and astigmatisms.The structure of UMS light path make Δ z＜＜R, this moment, spherical aberration and coma were much littler than astigmatism.Be the control image quality, object lens is generally all smaller from the axle incident angle in the UMS light path, and in 10 °, the astigmatism in this moment UMS light path is than coma and big 2～4 one magnitude of spherical aberration, need consider emphatically in design that therefore astigmatism also proofreaies and correct.

Because the wave band at different trace gas characteristic absorption bands place is different, the receptivity power differs greatly, and the requirement of detection limit also is not quite similar.Therefore, the optimal absorption optical path length of various trace gas is different, does not wait from tens meters to several kms.For many light paths DOAS system, the light path number of UMS light path is variable very necessary.For different UMS light paths, changing the light path number all is to realize that through the adjustment object lens astigmatism value also can change.With a modified White light path is example, like Fig. 4, and the UMS light path of this variable light path; Astigmatism is optimized at 96 light path numbers; Under the different optical path said conditions be the hot spot output experiment effect of light source with laser, Fig. 4-1 is 24 light path numbers disperse situation of hot spots down, and Fig. 4-2 is 48 light path numbers disperse situation of hot spots down; Fig. 4-3 is the disperse situation of 72 following hot spots of light path number, and Fig. 4-4 is the disperse situation of 96 following hot spots of light path number.Can see that count under the situation at 24,48,72 light paths, hot spot because of different astigmatism situation disperse has taken place, and degree varies, the hot spot angle is also inequality.Under the different optical path said conditions, the UMS light path has different astigmatism performances, thereby influences the application in the system, must consider compensation.

In addition, for the UMS light path of fixed light number of passes, the situation of output astigmatic bundle is arranged also: at first, in the UMS light path design, often design parameter just can not guarantee zero astigmatism.Such as, for simple BHWC and PBWC light path, the spacing between near the imaging facula in two row input apertures the field lens must satisfy approximately

(like Fig. 5-1, Fig. 5-2, h input aperture is to Y _rTwo times of leaving of wheelbase, p for the input aperture to X _rThe distance of axle), could offset astigmatism.At this time, field lens needs bigger caliber size, and utilization ratio is very low.If reduce field lens, then need reduce spacing, astigmatism is just non-vanishing.Secondly, when regulating many optical-path light-paths, tend to depart from optimal design and export astigmatic bundle.Astigmatic bundle through the output of subsequent optical path compensation UMS light path is necessary very much.

At present the astigmatic compensation of UMS light path lacks suitable theoretical method and because the modification inconvenience of software trace, need provide initial value to be optimized in just being implemented among a small circle and cause it not have suitable numerical computation method.Researchers analyze the often poor effect of astigmatic compensation and too big to the restriction of analytic target of Research on compensation method result for astigmatism; Lack versatility; Precision is low; Be difficult to for the optimization of UMS light path provides strong help, and analyze in the compensation method, be difficult to directly the UMS light path carried out astigmatic compensation with ray-tracing software at traditional astigmatism.

Summary of the invention

The objective of the invention is to design the subsequent optical path of UMS light path, this light path can realize the function of UMS astigmatic compensation.

The invention is characterized in:

Contain following step successively:

Step (1): to the many optical-path light-paths of unit enlargement ratio of a setting, be called for short the UMS light path, down together, calculate following each parameter through the chief ray trace:

The unit vector r of this UMS light path emergent ray _In,

The last meridian ellipse normal vector n that on object lens, reflects _eAnd the equivalent astigmatism thin lens rotation angle α of this secondary reflection,

The parameter beta of rotation matrix E and the eigenvalue of this rotation matrix _sAnd λ _m, and λ _m-λ _sIt is exactly the aberration of this UMS light path;

Step (2): the radius-of-curvature of setting compensation spherical mirror is r; Beam divergence angle amplifies a doubly before ratio is proofreaied and correct after correction; Said compensation spherical mirror is placed on after the output aperture of said UMS light path, so that through regulating said compensation spherical mirror, makes both astigmatisms complementary.

Export reference surface and the approximate value that compensates spherical mirror by the approximate light beam of obtaining this UMS light path of Gauss formula apart from l:

$l=(1+a)\frac{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000506963600022.png,HSA00000506963600051.png"\; state="\{\{state\}\}">r</figure-callout>}}{2}$

Step (3): said two eigenvalue of the said rotation matrix E of UMS light path when not carrying out astigmatic compensation _sAnd λ _mAnd the diagonal entry e of said rotation matrix E ₁₁And e ₂₂Rotation matrix E when calculate considering astigmatic compensation " two eigenvalue ₁And λ ₂:

${\mathrm{\&lambda;}}_1=\max ({\mathrm{\&lambda;}}_m,{\mathrm{\&lambda;}}_s)=\frac{{\mathrm{<figure-callout\; id="11"\; label="e"\; filenames="HSA00000506963600061.png"\; state="\{\{state\}\}">e</figure-callout>}}_{11}+e_{22}+\sqrt{{(e_{11}-e_{22})}^2+{4e}_{12}^2}}{2}$

${\mathrm{\&lambda;}}_2=\mathrm{Min}({\mathrm{\&lambda;}}_m,{\mathrm{\&lambda;}}_s)=\frac{{\mathrm{<figure-callout\; id="11"\; label="e"\; filenames="HSA00000506963600061.png"\; state="\{\{state\}\}">e</figure-callout>}}_{11}+e_{22}-\sqrt{{(e_{11}-e_{22})}^2+{4e}_{12}^2}}{2},$ Wherein:

$E=\left[\begin{array}{cc}{e}_{11}& e_{12}\\ e_{12}& e_{22}\end{array}\right]=\left[\begin{array}{cc}{\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000506963600022.png,HSA00000506963600051.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&beta;}{\mathrm{\&lambda;}}_s+{\sin }^2\mathrm{\&beta;}{\mathrm{\&lambda;}}_m& ({\mathrm{\&lambda;}}_s-{\mathrm{\&lambda;}}_m)\sin \mathrm{\&beta;}\cos \mathrm{\&beta;}\\ ({\mathrm{\&lambda;}}_s-{\mathrm{\&lambda;}}_m)\sin \mathrm{\&beta;}\cos \mathrm{\&beta;}& {\sin }^2\mathrm{\&beta;}{\mathrm{\&lambda;}}_s+{\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000506963600022.png,HSA00000506963600051.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&beta;}{\mathrm{\&lambda;}}_m\end{array}\right]$

Step (4), β and two eigenvalue of obtaining according to step (3) ₁And λ ₂, be calculated as follows the rotation angle α that said compensation spherical mirror reflects equivalent astigmatism _c:

λ _s＞λ _mThe time, α _c=β,

λ _s＜λ _mThe time, ${\mathrm{\&alpha;}}_c=\mathrm{\&beta;}+\frac{\mathrm{\&pi;}}{2},$

Step (5), β and two eigenvalue of obtaining according to step (3) ₁And λ ₂, be calculated as follows the incident angle θ of the output beam of said UMS light path to said compensation spherical mirror:

$\cos \mathrm{\&theta;}=\frac{-\mathrm{\&tau;}+\sqrt{{\mathrm{\&tau;}}^2+16}}{4},$ $\mathrm{\&tau;}=\frac{r}{{\mathrm{\&lambda;}}_2+l}-\frac{r}{{\mathrm{\&lambda;}}_1+l},$

Step (6) is according to resulting α and α _cBe calculated as follows the rotation angle of said compensation spherical mirror reflection meridian ellipse to the meridian ellipse of the last object lens reflection of said UMS light path

Step (7) is found the solution the normal direction vector n that the compensation spherical mirror reflects meridian ellipse by following formula _c:

$r_{\mathrm{in}}=s_g\frac{n_e\&times;n_c}{\left|\right|n_e\&times;n_c\left|\right|}$

* be meant multiplication cross computing, s _gBe sign:

When reflecting even number time in the UMS light path altogether, coordinate system is a right-handed coordinate system, s _g=1,

When reflecting odd number time in the UMS light path altogether, coordinate system is a left-handed coordinate system, s _g-1;

N ' unit vector:

$n^{\&prime;}=\frac{n_e\&times;r_{\mathrm{in}}}{\left|\right|n_e\&times;r_{\mathrm{in}}\left|\right|},$

Step (8) is calculated as follows the radius-of-curvature of said compensation spherical mirror | r _DC| direction vector r _DCAnd the direction vector r of reflection ray _Ref:

$r_{\mathrm{DC}}=\left(\sin \mathrm{\&theta;}\right)\frac{r_m\&times;n_c}{\left|\right|r_{\mathrm{in}}\&times;n_c\left|\right|}-\left(\cos \mathrm{\&theta;}\right)r_{\mathrm{in}}$

$r_{\mathrm{ref}}=\left(\sin 2\mathrm{\&theta;}\right)\frac{r_{\mathrm{in}}\&times;n_c}{\left|\right|r_{\mathrm{in}}\&times;n_c\left|\right|}-\left(\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000506963600022.png,HSA00000506963600051.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&theta;}\right)r_{\mathrm{in}}.$

A kind of many optical-path light-paths of enlargement ratio system of unit with follow-up astigmatic compensation function that described unit many optical-path light-paths of enlargement ratio astigmatic compensation method constructs is characterized in that described UMS light path is the BHWC light path, and its input and output aperture is positioned over the center of curvature plane homonymy of object lens and field lens; And cut into T-shape to field lens; Concrete parameter is the distance R=625mm between object lens and field lens, and input aperture centre coordinate is (h/2, p; 0), wherein h/2 is input aperture centre distance Y _rThe distance of axle, p is input aperture centre distance X _rThe distance of axle, p=40mm, h=20mm, Δ is the horizontal range of object lens center to self center of curvature, Δ=50mm, light path is counted n=40, and the radius-of-curvature of compensation spherical mirror is r=200mm, beam divergence angle adjustment multiple a=(1: 1)～(3: 1).

A kind of many optical-path light-paths of enlargement ratio system of unit that described unit many optical-path light-paths of enlargement ratio astigmatic compensation method constructs with follow-up astigmatic compensation function; It is characterized in that; Described UMS light path is follow-on White light path, numerical aperture NA=0.05,, radius-of-curvature is R=750mm; The radius-of-curvature of compensation spherical mirror is r=200mm; Δ is the horizontal range of object lens center to self center of curvature, Δ=56mm, beam divergence angle adjustment multiple a=(1: 1) or a=(2: 1).

Effect of the present invention is: the reflection compensation mirror is used for effectively reducing the astigmatism of UMS light path after the many optical-path light-paths of unit enlargement ratio, thereby effectively reduces the imaging facula size of UMS light path, improves its image quality.

Description of drawings

Fig. 1: UMS light path system.

1-1:UMS light path synoptic diagram, F are field lens, and M is object lens, and subscript is the sequence number of object lens, and R is the distance between object lens and the field lens, EA _InBe input aperture, EA _OutBe the output aperture.

1-2:UMS light path object lens view.

1-3:UMS light path field lens view, EA _InBe input aperture, EA _OutBe the output aperture, FT is the field lens of T shape bore, and FR is the field lens of rectangle bore, and FP is corner cube mirror or prism.

Fig. 2: several kinds of UMS light paths commonly used.

2-1:BHWC light path synoptic diagram, wherein F is a field lens, M ₁, M ₂Be object lens, EA _InBe input aperture, EA _OutBe the output aperture.

2-2:PBWC light path synoptic diagram, wherein F is a field lens, M ₁, M ₂Be object lens, EA _InBe input aperture, EA _OutBe the output aperture.

2-3: modified White light path synoptic diagram, F ₁Be field lens, FP is a corner cube mirror, M ₁, M ₂Be object lens, EA _InBe input aperture, EA _OutBe the output aperture.

2-4: modified White light path synoptic diagram, F is a field lens, FP is a corner cube mirror, M ₁, M ₂Be object lens, EA _InBe input aperture, EA _OutBe the output aperture.

2-5:MMS light path synoptic diagram, F ₁, F ₂Be field lens, M ₁, M ₂, M ₃Be object lens, EA _InBe input aperture, EA _OutBe the output aperture.

Fig. 3: the aberration diagram of spherical mirror imaging, extra-axial object point is P, object point is A on the axle; Y is an object height; O is the sphere summit, and C is the centre of sphere, and Iz is that axle is gone up the distance of some A to centre of sphere C; A ' goes up the light process spherical mirror reflection back and optical axis u, the intersection point of u ' that some A sends for axle.R is a sphere i ' mirror radius, and l is the object space intercept, and h is the light rise, is respectively object space aperture angle and picture side's aperture angle, and i is an incident angle, is reflection angle, i _pBe extra-axial object point P and the line PO of sphere summit O and the angle of optical axis.

Fig. 4: modified White light path is counted the hot spot experimental result picture of the output under the situation at different light paths.

Fig. 5: typical UMS light path synoptic diagram.

The BHWC light path synoptic diagram of 5-1:16 light path number, wherein F is a field lens, C _FBe the field lens center of curvature, M ₁, M ₂Be object lens, C ₁And C ₂Be respectively both centers of curvature, EA _InBe input aperture, EA _OutBeing the output aperture, 1.～7. is the imaging facula in the input aperture on field lens surface successively, and O is the three-dimensional cartesian coordinate system X that makes up _r-Y _r-Z _rInitial point, the input aperture two the row imaging faculas spacing be h,

D_Dd_, Z _r) in this plane, C ₁The distance that arrives P is at Y _rProjection on the axle.

The PBWC light path synoptic diagram of 5-2:18 light path number, wherein F is a field lens, C _FBe the field lens center of curvature, M ₁, M ₂Be object lens, C ₁And C ₂Be respectively both centers of curvature, EA _InBe input aperture, EA _OutBeing the output aperture, 1.～8. is the imaging facula in the input aperture on field lens surface successively, and O is the three-dimensional cartesian coordinate system X that makes up _r-Y _r-Z _rInitial point, the input aperture two the row imaging faculas spacing be h,

D_Dd__________________

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

5-3: the front elevation of modified White light path field lens, wherein FT is " T " shape field lens, FP is a corner cube mirror, C ₁And C ₂Be respectively object lens M ₁, M ₂The center of curvature, EA _InBe input aperture, EA _OutBe the output aperture, 66666666666 Fig. 6: the synoptic diagram of astigmatism is offset in the complementation imaging of bispheric lens, and O and O ' are spherical mirror, and D and D ' are respectively the summits of spherical mirror, and C and C ' are the centers of curvature of spherical mirror; P and P ' are respectively object point and picture point, and M is respectively meridian picture and the sagitta of arc picture that P is become by spherical mirror O with S.

Fig. 7: compensation spherical mirror synoptic diagram, wherein 1 is the UMS image planes, 2 is UMS output aperture EA _Out, the center of curvature of compensation spherical mirror Mc is C, culminating point is D, supposes its radius-of-curvature CD=r; Along on the chief ray direction of propagation, the light beam of UMS light path output reference surface PExit is l, i.e. P to the distance of compensating glass _ExitD=l, θ are the incident angle of light beam to compensating glass.

Fig. 8: the parameter of compensation spherical mirror is confirmed flow process.

Fig. 9: have the UMS light path that compensates spherical mirror.

9-1: have the BHWC index path that compensates spherical mirror, Mc is the compensation spherical mirror.

9-2: have the PBWC index path that compensates spherical mirror, Mc is the compensation spherical mirror.

9-3: have the modified White index path that compensates spherical mirror, Mc is the compensation spherical mirror, and PQ is a corner cube mirror.

9-4: have the modified White index path that compensates spherical mirror, Mc is the compensation spherical mirror, and PQ1 and PQ2 are corner cube mirror, and the spacing of the object lens center of curvature is c, and the input aperture is mirror F in the home court ₁On the column pitch and the line space of imaging facula be respectively 2c and l.

9-5: have the MMS index path that compensates spherical mirror, Mc is the compensation spherical mirror.

Figure 10: the imaging facula point range figure before the BHWC light path astigmatic compensation.

Figure 11: have the BHWC light channel structure figure that compensates spherical mirror.

Figure 12: the imaging facula point range figure (a=1) behind the BHWC light path astigmatic compensation.

Figure 13: BHWC optical path compensation spherical mirror parameter and imaging facula RMS radius, wherein ■ is an astigmatism before the compensation, ▲ be imaging RMS radius before the compensation, ◆ be compensation back imaging RMS radius.

Figure 14: have the modified White light channel structure figure that compensates spherical mirror, S is an xenon lamp.

Figure 15: the imaging facula RMS radius behind the astigmatic compensation during different a, wherein ■ is a=1, ▲ be a=2.

Embodiment

Subject matter of the present invention is to provide the UMS light path to resolve the astigmatism computing method accurately; And to concrete light path such as BHWC light path; PBWC light path and modified White light path provide approximate astigmatism analytic formula; Problem to the astigmatic compensation poor effect of UMS light path; Take and two similar thinkings of the corresponding astigmatism that disappears of spherical reflector meridian ellipse-sagittal surface, designed a kind of follow-up astigmatic compensation light path of UMS light path, this light path utilizes a spherical mirror to realize the function of astigmatic compensation as the UMS subsequent optical path; According to light path accurate Analysis astigmatism computing method, establish theoretical astigmatism and be parameter such as anti-position that solves the compensatory reflex spherical mirror and angle under zero the situation.

Be the accurate parsing astigmatism computing method of UMS light path below; This optical matrix that utilizes; The method that the optical system equivalence is calculated astigmatism then for astigmatism thin lens sequence is applicable to various UMS light paths, comprises White light path (BHWC light path, PBWC light path etc.); Various modified White light paths, MMS light path etc.

The accurate Analysis astigmatism of UMS light path can be drawn by optical matrix, and the nonaxisymmetrical centered optical system of UMS light path can be expressed as one 4 * 4 optical matrix under the condition of paraxial approximation

$M=\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]$

Wherein, A, B, C, D are 2 * 2 partitioned matrix, and Metzler matrix is decomposed into following form:

$M=\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]=\left[\begin{array}{cc}I& E\\ 0& I\end{array}\right]\left[\begin{array}{cc}0& F\\ F^{*}& 0\end{array}\right]\left[\begin{array}{cc}I& G\\ 0& I\end{array}\right],$

E=AC wherein ^-1, G=A ^-1D, F ^*=C, F=B-AC ^-1D=(C ^T) ^-1

Two eigenvalue of E _sAnd λ _mJust in time characterized the distance of the meridian and the sagitta of arc bifocal system of distance output reference surface of emergent ray.According to the definition of light pencil astigmatism, the value that can obtain astigmatism is:

l _sm＝(-λ _s)-(-λ _m)＝λ _m-λ _s

If E is decomposed and can get:

$E=\left[\begin{array}{cc}{e}_{11}& e_{12}\\ e_{12}& {\mathrm{<figure-callout\; id="22"\; label="e"\; filenames="HSA00000506963600082.png"\; state="\{\{state\}\}">e</figure-callout>}}_{22}\end{array}\right]=S(-\mathrm{\&beta;})\left[\begin{array}{cc}{\mathrm{\&lambda;}}_s& 0\\ 0& {\mathrm{\&lambda;}}_m\end{array}\right]S\left(\mathrm{\&beta;}\right)$

$=\left[\begin{array}{cc}{\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000506963600022.png,HSA00000506963600051.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&beta;}{\mathrm{\&lambda;}}_s+{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000506963600022.png,HSA00000506963600051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}{\mathrm{\&lambda;}}_m& ({\mathrm{\&lambda;}}_s-{\mathrm{\&lambda;}}_m)\sin \mathrm{\&beta;}\cos \mathrm{\&beta;}\\ ({\mathrm{\&lambda;}}_s-{\mathrm{\&lambda;}}_m)\sin \mathrm{\&beta;}\cos \mathrm{\&beta;}& {\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000506963600022.png,HSA00000506963600051.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&beta;}{\mathrm{\&lambda;}}_s+{\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000506963600022.png,HSA00000506963600051.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&beta;}{\mathrm{\&lambda;}}_m\end{array}\right]$

Wherein: $S\left(\mathrm{\&beta;}\right)=\left[\begin{array}{cc}\mathrm{Cos}\mathrm{\&beta;}& \mathrm{Sin}\mathrm{\&beta;}\\ -\mathrm{Sin}\mathrm{\&beta;}& \mathrm{Cos}\mathrm{\&beta;}\end{array}\right]$

The abbreviation arrangement obtains:

$l_{\mathrm{sm}}=\sqrt{{(e_{11}-e_{22})}^2+{4\mathrm{<figure-callout\; id="12"\; label="e"\; filenames="HSA00000506963600061.png,HSA00000506963600081.png"\; state="\{\{state\}\}">e</figure-callout>}}_{12}^2}$

Simplify to concrete light path resolving astigmatism accurately, be similar to and obtain following astigmatism computing formula, provide the BHWC light path below, PBWC light path, a kind of approximate analysis astigmatism of modified White light path.

Be depicted as the BHWC light path of 16 light path numbers like Fig. 5-1, the BHWC light path is the UMS light path of a typical plane symmetry.Wherein, F is a field lens, and the center of curvature is C _FM ₁And M ₂Be two sphere object lens, their center of curvature is respectively C ₁And C ₂EA _InExpression input aperture; EA _OutThe expression output aperture.1.～7. be the imaging facula in the input aperture on field lens surface successively.For conveniently carrying out parameter declaration, in synoptic diagram, set up a three-dimensional cartesian coordinate system X _r-Y _r-Z _r, its initial point is O.Subscript r be for front equivalence astigmatism model in coordinate system distinguish mutually.C _FWith culminating point all at Z _rOn the axle, C ₁And C ₂At Y _rOn the axle.

For a light path number is the BHWC light path of n (n is 4 multiple), and the coordinate of input aperture center is (h/2, p, 0), C _FCoordinate be (0,0, R), C ₁And C ₂Be respectively (0, c/2,0) and (0 ,-c/2,0), c=4p/n.The spacing of the two row imaging faculas in input aperture is h.System's aperture is positioned at M ₁, the centre coordinate of entrance pupil be P (0, Δ+c/2, (R ²-Δ ²) ^1/2).Plane X _rOZ _rBe the symmetrical plane of BHWC light path, just in time divide the two row imaging faculas in these input apertures equally.

Its approximate analysis astigmatism is:

$l_{\mathrm{sm}}=\frac{n}{R}(\frac{{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HSA00000506963600022.png,HSA00000506963600051.png"\; state="\{\{state\}\}">p</figure-callout>}}^2}{3}-\frac{{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HSA00000506963600022.png,HSA00000506963600051.png"\; state="\{\{state\}\}">h</figure-callout>}}^2}{4})-\frac{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HSA00000506963600022.png,HSA00000506963600051.png"\; state="\{\{state\}\}">n</figure-callout>}}^2\mathrm{p\&Delta;}}{30R^3}({5\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HSA00000506963600022.png,HSA00000506963600051.png"\; state="\{\{state\}\}">h</figure-callout>}}^2+2p^2)$

Fig. 5-2 is the PBWC light path of 18 light path numbers, and this is typical asymmetric UMS light path, and wherein, F is a field lens, C _FIt is the center of curvature; M ₁And M ₂Be two sphere object lens, their center of curvature is respectively C ₁And C ₂EA _InExpression input aperture; EA _OutThe expression output aperture.1.～8. be the imaging facula in the input aperture on field lens surface successively.For conveniently carrying out parameter declaration, in synoptic diagram, set up a three-dimensional cartesian coordinate system X _r-Y _r-Z _r, its initial point is O.Subscript r be for front equivalence astigmatism model in coordinate system distinguish mutually.C _FWith culminating point all at Z _rOn the axle, C ₁And C ₂At Y _rOn the axle.

For a light path number is the PBWC light path of n (n=4x+2, x are integer), and the coordinate of input aperture center is (h/2, p, 0), C _FCoordinate be (0,0, R), C ₁And C ₂Be respectively (0,0,0) and (0 ,-c, 0), c=4p/ (n-2).The spacing of the two row imaging faculas in input aperture is h.System's aperture is positioned at M ₁, the centre coordinate of entrance pupil be P (0, Δ, (R ²Δ ²) ^1/2).Different with the BHWC light path, plane X _rOZ _rIt no longer is the symmetrical plane of PBWC light path.

Its approximate analysis astigmatism is:

$l_{\mathrm{sm}}=\frac{n(n+2)}{3(n-2)R}{p}^2-\frac{n}{4R}{h}^2-\frac{\mathrm{np\&Delta;}}{30R^3}[\frac{2({\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HSA00000506963600022.png,HSA00000506963600051.png"\; state="\{\{state\}\}">n</figure-callout>}}^2+4)(n+2)}{{(n-2)}^2}{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HSA00000506963600022.png,HSA00000506963600051.png"\; state="\{\{state\}\}">p</figure-callout>}}^2+5(n+2)h^2]$

Complicated UMS light path comprises modified White light path and MMS light path, and the imaging facula in its input aperture is array distribution near field lens, and promptly image patch is more than 2 row.Complicated UMS light path can be regarded the stack of a plurality of BHWC light paths or PBWC light path as.For simplicity, its system's astigmatism then can be regarded the simple superposition of a plurality of BHWC light paths or PBWC light path as.

Fig. 5-the 3rd, the front elevation of follow-on White light path, its approximate analysis astigmatism is:

$l_{\mathrm{sm}}=\frac{1}{6}\frac{n}{R}({4p}^2-15l^2)+\frac{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HSA00000506963600022.png,HSA00000506963600051.png"\; state="\{\{state\}\}">n</figure-callout>}}^2\mathrm{p\&Delta;}}{15R^3}(2{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HSA00000506963600022.png,HSA00000506963600051.png"\; state="\{\{state\}\}">p</figure-callout>}}^2+25l^2)$

The complementary imaging of the astigmatic compensation thinking of UMS light path and bispheric lens is similar, as shown in Figure 6, and O and O ' are spherical mirror, and D and D ' are respectively the summits of spherical mirror, and C and C ' are the centers of curvature of spherical mirror; P and P ' are respectively object point and picture point, and M is respectively meridian picture and the sagitta of arc picture that P is become by spherical mirror O with S.Total astigmatism is zero when spherical mirror O ' and O complementation imaging: at this moment, plane P DC is the meridian ellipse of spherical mirror O imaging, just in time also is the sagittal surface of spherical mirror O ' imaging; And plane P ' D ' C ' is the sagittal surface of spherical mirror O imaging, the meridian ellipse of spherical mirror O ' imaging; Meridian image distance, the sagitta of arc image distance of spherical mirror O imaging equate with the sagitta of arc object distance and the meridian object distance of sphere O ' imaging respectively, i.e. DM=SD ', DS=MD '.If consider that light path is reversible, when P ' was object point, S and M then just in time were the meridian picture and the sagitta of arc pictures of spherical mirror O ' imaging.Introducing a compensation spherical mirror is placed on after the output aperture of UMS light path; Through regulating the compensation spherical mirror; Make the whole imaging effect of itself and UMS light path complementary: the output beam of UMS light path reflects on this spherical mirror; And the reflection meridian ellipse just in time overlaps with the sagittal surface of UMS light path output beam, astigmatism just in time with the astigmatism equal and opposite in direction of UMS light path output beam, opposite in sign.Except that compensating astigmatism; The compensation spherical mirror can further be regulated the output beam angle of divergence; Make the numerical aperture (numerical aperture of small light spectrometer is bigger than UMS light path, generally between 0.1～0.22) of itself and subsequent optical spectrometer system be complementary the coupling link of simplified system.

Draw l according to this thinking and preceding text UMS light path accurate Analysis astigmatism computing method _Sm=(λ _s)-(-λ _m)=λ _m-λ _s, we only need make E matrix two eigenwerts of the optical system that has added the compensation spherical mirror equate, so just can instead on this basis solve the parameter of compensation spherical mirror.

Like Fig. 7, the center of curvature of compensation spherical mirror Mc is C, and culminating point is D, supposes its radius-of-curvature CD=r; Along on the chief ray direction of propagation, the light beam of UMS light path output reference surface P _ExitDistance to compensating glass is l, i.e. P _ExitD=l.Here light beam output reference surface P _ExitBe defined as the equidistance bisector plane of UMS light path meridian picture and sagitta of arc picture, light beam is exported reference surface and is set to coincide with the output aperture of UMS light path in the UMS of variable light path light path.

The E matrix of supposing the UMS light path does

$E=\left[\begin{array}{cc}{e}_{11}& e_{12}\\ e_{12}& {\mathrm{<figure-callout\; id="22"\; label="e"\; filenames="HSA00000506963600082.png"\; state="\{\{state\}\}">e</figure-callout>}}_{22}\end{array}\right]=S(-\mathrm{\&beta;})\left[\begin{array}{cc}{\mathrm{\&lambda;}}_s& 0\\ 0& {\mathrm{\&lambda;}}_m\end{array}\right]S\left(\mathrm{\&beta;}\right)---(1-1)$

The equivalent astigmatism thin lens rotation angle of last object lens reflection is α.

Obviously have

λ _m-λ _s＝(e ₂₂-e ₁₁)cos2β-2e ₁₂sin2β

λ _m+λ _s＝e ₁₁+e ₂₂ (1-2)

$\mathrm{\&beta;}=\frac{1}{2}\arctan \left(\frac{{2e}_{12}}{e_{11}-e_{22}}\right)$

Try to achieve

λ _m＝e ₁₁sin ²β+e ₂₂cos ²β-e ₁₂sin2β

λ _s＝e ₁₁cos ²β+e ₂₂sin ²β+e ₁₂sin2β

Through the propagation of free distance l and by after the compensating glass reflection, the E matrix becomes

E′＝((E+lI) ^-1+L _c) ^-1 (1-4)

Wherein

$L_c=S\left({-\mathrm{\&alpha;}}_c\right)\left[\begin{array}{cc}-\frac{2\cos \mathrm{\&theta;}}{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HSA00000506963600021.png,HSA00000506963600041.png"\; state="\{\{state\}\}">r</figure-callout>}}& 0\\ 0& -\frac{2}{r\cos \mathrm{\&theta;}}\end{array}\right]S\left({\mathrm{\&alpha;}}_c\right)$

θ is the incident angle of light beam to compensating glass, α _cIt is the equivalent astigmatism thin lens rotation angle of compensating glass reflection.

Formula (1-1) substitution formula (1-4) is had:

E′＝S(-β)E″S(β) (1-5)

Wherein

$E^{\&prime;\&prime;}=\left[\begin{array}{cc}\frac{1}{{\mathrm{\&lambda;}}_s+\mathrm{<figure-callout\; id="0"\; label="l"\; filenames="HSA00000506963600021.png,HSA00000506963600041.png"\; state="\{\{state\}\}">l</figure-callout>}}& 0\\ 0& \frac{1}{{\mathrm{\&lambda;}}_m+l}\end{array}\right]+S(\mathrm{\&beta;}-{\mathrm{\&alpha;}}_c)\left[\begin{array}{cc}-\frac{2\cos \mathrm{\&theta;}}{r}& \mathrm{\&theta;}\\ 0& -\frac{2}{r\cos \mathrm{\&theta;}}\end{array}\right]S({\mathrm{\&alpha;}}_c-\mathrm{\&beta;})$

Formula l according to the astigmatism of trying to achieve in the preceding text _Sm=(λ _s)-(-λ _m)=λ _m-λ _sKnow; Two eigenwerts of the E matrix E of the integral body of the UMS light path after the adding compensatory reflex mirror must equate that could satisfy theoretic astigmatism according to the astigmatism formula like this is zero, thereby reach the purpose of astigmatic compensation; Therefore E " also has two equal eigenwerts, must be $\left[\begin{array}{cc}\mathrm{\&lambda;}& 0\\ 0& \mathrm{\&lambda;}\end{array}\right]$ Form, need to satisfy:

$\left\{\begin{array}{c}\frac{1}{{\mathrm{\&lambda;}}_s+l}-\frac{2\cos \mathrm{\&theta;}}{r}=\frac{1}{{\mathrm{\&lambda;}}_m+l}-\frac{2}{r\cos \mathrm{\&theta;}},{\mathrm{\&alpha;}}_c=\mathrm{\&beta;}({\mathrm{\&lambda;}}_s>{\mathrm{\&lambda;}}_m)\\ \frac{1}{{\mathrm{\&lambda;}}_s+l}-\frac{2}{r\cos \mathrm{\&theta;}}=\frac{1}{{\mathrm{\&lambda;}}_m+l}-\frac{2\cos \mathrm{\&theta;}}{r},{\mathrm{\&alpha;}}_c=\mathrm{\&beta;}+\frac{\mathrm{\&pi;}}{2}({\mathrm{\&lambda;}}_s<{\mathrm{\&lambda;}}_m)\end{array}\right.---(1-6)$

Do not consider λ in the formula (1-6) _s=λ _mSituation because the astigmatism of UMS light path is 0 in this case, do not need the compensation.β substitution formula (1-3) with in the formula (1-2) has:

${\mathrm{\&lambda;}}_1=\max ({\mathrm{\&lambda;}}_m,{\mathrm{\&lambda;}}_s)=\frac{{\mathrm{<figure-callout\; id="11"\; label="e"\; filenames="HSA00000506963600061.png"\; state="\{\{state\}\}">e</figure-callout>}}_{11}+{\mathrm{<figure-callout\; id="22"\; label="e"\; filenames="HSA00000506963600082.png"\; state="\{\{state\}\}">e</figure-callout>}}_{22}+\sqrt{{(e_{11}-e_{22})}^2+{4\mathrm{<figure-callout\; id="12"\; label="e"\; filenames="HSA00000506963600061.png,HSA00000506963600081.png"\; state="\{\{state\}\}">e</figure-callout>}}_{12}^2}}{2}$ (1-7)

${\mathrm{\&lambda;}}_2=\min ({\mathrm{\&lambda;}}_m,{\mathrm{\&lambda;}}_s)=\frac{{\mathrm{<figure-callout\; id="11"\; label="e"\; filenames="HSA00000506963600061.png"\; state="\{\{state\}\}">e</figure-callout>}}_{11}+e_{22}-\sqrt{{(e_{11}-e_{22})}^2+{4\mathrm{<figure-callout\; id="12"\; label="e"\; filenames="HSA00000506963600061.png,HSA00000506963600081.png"\; state="\{\{state\}\}">e</figure-callout>}}_{12}^2}}{2}$

Consider formula (1-6) again, then have:

$\frac{1}{{\mathrm{\&lambda;}}_1+l}-\frac{2\cos \mathrm{\&theta;}}{r}=\frac{1}{{\mathrm{\&lambda;}}_2+l}-\frac{2}{r\cos \mathrm{\&theta;}}---(1-8)$

Make

formula (1-8) can be organized into equation

2cos ²θ+τcosθ-2＝0 (1-9)

Because | cos θ |≤1, quadratic equation with one unknown (1-9) has only one to separate meaningful:

$\cos \mathrm{\&theta;}=\frac{-\mathrm{\&tau;}\sqrt{{\mathrm{\&tau;}}^2+16}}{4}---(1-10)$

The size of l is decided by the radius-of-curvature r of compensation spherical mirror and the multiple a of beam divergence angle adjustment.Come to find the solution approx with Gauss's imaging formula:

1/l+1/l′＝2/r

(1-11)

l′/l′＝1/a

Trying to achieve l is approximately

$l=(1+a)\frac{r}{2}---(1-12)$

Like Fig. 7, the meridian ellipse normal vector that UMS reflects on object lens for the last time is n _e, the direction vector of reflection ray is r _In, find the solution the meridian ellipse normal vector n of compensation spherical mirror reflection with this _cn _e, r _In, n _cAll be unit vector, calculating them and satisfy by optical matrix

$r_{\mathrm{in}}=s_g\frac{n_e\&times;n_c}{\left|\right|n_e\&times;n_c\left|\right|}---(1-13)$

* be meant multiplication cross computing, s _gIt is sign.When reflecting even number time in the UMS light path altogether, coordinate system is a right-handed coordinate system, s _g=1; When reflecting odd number time in the UMS light path altogether, coordinate system is a left-handed coordinate system, s _g=-1.Situation among Fig. 7 is a left-handed coordinate system, below derives all in view of the situation

Like Fig. 7 vector n _cAnd n _eBetween angle do

Supposing has unit vector

$n^{\&prime;}=\frac{n_e\&times;r_{\mathrm{in}}}{\left|\right|n_e\&times;r_{\mathrm{in}}\left|\right|}---(1-15)$

The vector projection relation is arranged again

(1-16)

Therefore compensate the normal direction n of the meridian ellipse of spherical mirror reflection _cFor:

The direction vector of DC and the direction vector of reflection ray can similarly be tried to achieve:

$r_{\mathrm{DC}}=\left(\sin \mathrm{\&theta;}\right)\frac{r_m\&times;n_c}{\left|\right|r_{\mathrm{in}}\&times;n_c\left|\right|}-\left(\cos \mathrm{\&theta;}\right)r_{\mathrm{in}}$

$r_{\mathrm{ref}}=\left(\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000506963600022.png,HSA00000506963600051.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&theta;}\right)\frac{r_{\mathrm{in}}\&times;n_c}{\left|\right|r_{\mathrm{in}}\&times;n_c\left|\right|}-\left(\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000506963600022.png,HSA00000506963600051.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&theta;}\right)r_{\mathrm{in}}---(1-18)$

Can be by following formula in the hope of the position of center of curvature C of compensation spherical mirror, according to the coordinate of culminating point D, can be in the hope of the corner information of compensation spherical mirror.

To sum up, the radius-of-curvature r of known compensation spherical mirror, the adjustment multiple a of the output beam angle of divergence, and the light path parameter of UMS light path, the position and the corner parameter of definite compensation spherical mirror, the practical implementation flow process of its method is as shown in Figure 8:

1, through the UMS light path is carried out the chief ray trace, calculates the unit vector r of UMS light path emergent ray _In, the meridian ellipse normal vector n that on object lens, reflects for the last time _e, and the equivalent astigmatism thin lens rotation angle α of this secondary reflection, calculate the E matrix simultaneously.The E matrix is carried out feature decomposition, can obtain the parameter beta and the eigenvalue of rotation matrix ₁And λ ₂, both differences are exactly the astigmatism of UMS light path;

2, the radius of curvature of known compensation spherical mirror is r; Doubly (lateral magnification 1/a) to compare amplification a after beam divergence angle is proofreaied and correct and before proofreading and correct; Based on Gauss formula can be similar to try to achieve the light beam output plane of reference and compensation spherical mirror apart from l, referring to formula (1-11) with (1-12);

3, according to β and eigenvalue ₁And λ ₂, can calculate the rotation angle α that compensating glass reflects equivalent astigmatism thin lens _c, referring to formula (1-4)～(1-6);

4, by parameter l, r, λ ₁And λ ₂Find the solution compensation spherical mirror angle of incidence of light θ, referring to formula (1-7)～(1-10);

5, by parameter alpha, α _cCalculate the rotation angle of compensation spherical mirror reflection meridian ellipse to the meridian ellipse of the last object lens reflection of UMS light path

And combination r _InAnd n _e, find the solution the normal direction of compensation spherical mirror reflection meridian ellipse, find the solution the position and the direction of compensation spherical mirror at last, referring to formula (1-13)～(1-18).

According to this compensation principle to before the UMS light path mentioned, such as the BHWC light path, the PBWC light path, modified White light path, and the MMS light path carries out astigmatic compensation, the whole light path synoptic diagram after its compensation is as shown in Figure 9.Fig. 9-1 carries out the whole light path behind the astigmatic compensation for the BHWC light path; Fig. 9-2 for the PBWC light path carry out after the astigmatic compensation whole light path; Fig. 9-3 is the whole light path after modified White light path is carried out astigmatic compensation; Fig. 9-3 carries out the whole light path behind the astigmatic compensation for another kind of modified White light path, and Fig. 9-5 carries out the whole light path behind the astigmatic compensation for the MMS light path, and wherein Mc is the compensatory reflex mirror.

The embodiment of this method is described through two specific embodiments at present.

White light path and modified White light path have a wide range of applications at the trace gas detection range, such as the vehicle exhaust SO in branch school, California, USA university streamside ₂The light path system of detector is exactly the White light path; The light path system of the instrument HR-DOAS of Germany Heidelberg university is a modified White light path; Also need use the UMS light path in other occasions that need repeatedly reflection to reach long light path; Two following examples are through respectively the modified White light path of BHWC light path and variable light path being carried out astigmatic compensation, through the effect before and after the emulation contrast compensation.

Embodiment one:

The BHWC light path

BHWC light path shown in Fig. 4-1, basic parameter are R=625mm, p=40mm, and h=20mm, Δ=50mm and n=40, its numerical aperture is NA=0.05.When not adopting the compensation of compensation spherical mirror, it is 24.8mm that calculating can get astigmatism.At this moment, 5 points of true field (0,0), imaging (Medial focus) the hot spot point range figure such as the Figure 10 of (± 0.5,0) and (0, ± 0.5), engineer's scale is 2000 μ m, its RMS radius is at 450～480 μ m.

The spherical mirror that adopts radius-of-curvature r=200mm is spherical mirror by way of compensation, and the system construction drawing after the compensation is shown in figure 11, and the system value aperture still is 0.05 constant, i.e. a=1.The parameter of compensation spherical mirror is referring to table 1.At this moment, 5 points of true field (0,0), the imaging facula point range figure such as the Figure 12 of (± 0.5,0) and (0, ± 0.5), engineer's scale are 200 μ m, its RMS radius is at 22～32 μ m, than not reduced at least 15 times before the compensation.

Embodiment two:

The modified White light path of variable light path

Shown in Fig. 2-3, be the modified White light path of one 96 light path numbers.Wherein, F ₁Be field lens, the center of curvature is C _FM ₁And M ₂Be two sphere object lens, their center of curvature is respectively C ₁And C ₂EA _InExpression input aperture; EA _OutThe expression output aperture.1.～

be the imaging facula in the input aperture on field lens surface successively.For conveniently carrying out parameter declaration, in synoptic diagram, set up a three-dimensional cartesian coordinate system X _r-Y _r-Z _r, its initial point is O.C _FWith culminating point all at Z _rOn the axle, C ₁And C ₂At Y _rOn the axle.

For a light path number is the BHWC light path of n (n is 4 multiple), C _FCoordinate be (0,0, R), C ₁And C ₂Be respectively (0, c/2,0) and (0 ,-c/2,0), c=4p/n.The spacing of the two row imaging faculas in input aperture is l.System's aperture is positioned at M ₁, the centre coordinate of entrance pupil be P (0, Δ+c/2, (R ²-Δ ²) ^1/2).When with object lens M ₂At Y _rOZ _r(X axle, Y axle are respectively through the catoptron center and are parallel to X around the X axle in the plane _rAxle, Y _rWhen the local coordinate axle of axle) direction is rotated, its center of curvature C ₂Along Y _rDirection of principal axis moves, and then the imaging facula on field lens surface also can move.If M ₂Rotate counterclockwise, imaging facula is to Y _rDirection moves, and 1. locates when 3. hot spot moves to hot spot, and the light path number becomes 84.In like manner, if CW rotates object lens M ₂The light path number is increased.This light path can realize the light path number of 12n ' (n ' for positive integer).The maximum optical number of passes is made as 96 times, and many optical-path light-paths system value aperture is NA=0.05.Radius of curvature R=750mm, Δ=56mm, when being maximum optical number of passes 96, the spot array line space equates all to be 12mm, i.e. 2c with column pitch ₉₆=12mm, l=12mm.Object lens center of curvature C ₁Coordinate be that (0 ,-3,0) immobilizes.Object lens M ₂With its summit (0, Δ, (R ²-Δ-c ₉₆/ 2) ^1/2) be the center, at Y _rOZ _rRotation makes the light path number variable between 12～96 in the plane.Figure 14 has provided when not compensating different light path numbers astigmatism situation down, and true field central field point (a=1, the astigmatism after the compensation is all less than 10 at the imaging point range figure RMS radius that compensates front and back ^-4Mm).

Table 2 has provided the compensation spherical mirror parameter of the variable and adjustment beam divergence angle multiple a=1 of light path several 12～96 and at 2 o'clock, and it is shown in figure 16 to add behind the compensating glass system light path of modified White light path, and the astigmatism value of compensation back light path is all 10 ^-4Below the mm, true field central field point imaging facula RMS radius is shown in figure 17.

With respect to the light path without astigmatic compensation, the image quality under different light path numbers of the light path behind the astigmatic compensation all is greatly improved: imaging RMS radius has reduced more than 20 times during a=1, and imaging RMS radius has then reduced more than 8 times during a=2.Image quality is comparatively balanced: during not compensated, the light path number is increased to 96 times from 12 times, and imaging facula RMS radius has increased by 431 μ m; Behind astigmatic compensation, the light path number is increased to 96 times from 12 times, and imaging facula RMS radius has only increased by 27 μ m (a=1) and 39 μ m (a=2) respectively, and amplification is less than the former 10%.

Therefore,, can obtain the new design that the astigmatic compensation mirror combines with the UMS light path, realize image quality comparatively balanced under the variable light path, reach the purpose that improves many optical-path light-paths performance based on the astigmatic compensation method of UMS.

Table 1

Table 2

Claims (3)

1. many optical-path light-paths of unit enlargement ratio astigmatic compensation method is characterized in that, contains following step successively:

Step (1): to the many optical-path light-paths of unit enlargement ratio of a setting, be called for short the UMS light path, down together, calculate following each parameter through the chief ray trace:

The unit vector r of this UMS light path emergent ray _In,

The last meridian ellipse normal vector n that on object lens, reflects _eAnd the equivalent astigmatism thin lens rotation angle α of this secondary reflection, the parameter beta of rotation matrix E and the eigenvalue of this rotation matrix _sAnd λ _m, and λ _m-λ _sIt is exactly the astigmatism of this UMS light path;

Step (2): the radius-of-curvature of setting compensation spherical mirror is r; Than amplifying a before proofreading and correct doubly, said compensation spherical mirror is placed on after the output aperture of said UMS light path beam divergence angle after correction, so that through regulating said compensation spherical mirror; Make both astigmatisms complementary, reach the effect of counteracting.

Obtain the approximate value apart from l of light beam output reference surface with the compensation spherical mirror of this UMS light path by Gauss formula:

$l=(1+a)\frac{r}{2};$

Step (3): said two eigenvalue of the said rotation matrix E of UMS light path when not carrying out astigmatic compensation _sAnd λ _mAnd the diagonal entry e of said rotation matrix E ₁₁And e ₂₂Rotation matrix E when calculate considering astigmatic compensation " two eigenvalue ₁And λ ₂:

${\mathrm{\&lambda;}}_1=\max ({\mathrm{\&lambda;}}_m,{\mathrm{\&lambda;}}_s)=\frac{e_{11}+e_{22}+\sqrt{{(e_{11}-e_{22})}^2+{4e}_{12}^2}}{2}$

${\mathrm{\&lambda;}}_2=\mathrm{Min}({\mathrm{\&lambda;}}_m,{\mathrm{\&lambda;}}_s)=\frac{e_{11}+e_{22}-\sqrt{{(e_{11}-e_{22})}^2+{4e}_{12}^2}}{2},$ Wherein:

$E=\left[\begin{array}{cc}{e}_{11}& e_{12}\\ e_{12}& e_{22}\end{array}\right]=\left[\begin{array}{cc}{\cos }^2\mathrm{\&beta;}{\mathrm{\&lambda;}}_s+{\sin }^2\mathrm{\&beta;}{\mathrm{\&lambda;}}_m& ({\mathrm{\&lambda;}}_s-{\mathrm{\&lambda;}}_m)\sin \mathrm{\&beta;}\cos \mathrm{\&beta;}\\ ({\mathrm{\&lambda;}}_s-{\mathrm{\&lambda;}}_m)\sin \mathrm{\&beta;}\cos \mathrm{\&beta;}& {\sin }^2\mathrm{\&beta;}{\mathrm{\&lambda;}}_s+{\cos }^2\mathrm{\&beta;}{\mathrm{\&lambda;}}_m\end{array}\right]$

Step (4), β and two eigenvalue of obtaining according to step (3) ₁And λ ₂, be calculated as follows the rotation angle α that said compensation spherical mirror reflects equivalent astigmatism _c:

λ _s＞λ _mThe time, α _c=β,

λ _s＜λ _mThe time, ${\mathrm{\&alpha;}}_c=\mathrm{\&beta;}+\frac{\mathrm{\&pi;}}{2},$

Step (5), β and two eigenvalue of obtaining according to step (3) ₁And λ ₂, be calculated as follows the incident angle θ of the output beam of said UMS light path to said compensation spherical mirror:

$\cos \mathrm{\&theta;}=\frac{-\mathrm{\&tau;}+\sqrt{{\mathrm{\&tau;}}^2+16}}{4},$ $\mathrm{\&tau;}=\frac{r}{{\mathrm{\&lambda;}}_2+l}-\frac{r}{{\mathrm{\&lambda;}}_1+l};$

Step (6) is according to resulting α and α _cBe calculated as follows the rotation angle of said compensation spherical mirror reflection meridian ellipse to the meridian ellipse of the last object lens reflection of said UMS light path

Step (7) is found the solution the normal direction vector n that the compensation spherical mirror reflects meridian ellipse by following formula _c:

$r_{\mathrm{in}}=s_g\frac{n_e\&times;n_c}{\left|\right|n_e\&times;n_c\left|\right|}$

* be meant multiplication cross computing, s _gBe sign:

When reflecting even number time in the UMS light path altogether, coordinate system is a right-handed coordinate system, s _g=1,

When reflecting odd number time in the UMS light path altogether, coordinate system is a left-handed coordinate system, s _g=-1;

N ' unit vector:

$n^{\&prime;}=\frac{n_e\&times;r_{\mathrm{in}}}{\left|\right|n_e\&times;r_{\mathrm{in}}\left|\right|};$

Step (8) is calculated as follows the radius-of-curvature of said compensation spherical mirror | r _DC| direction vector r _DCAnd the direction vector r of reflection ray _Ref:

$r_{\mathrm{DC}}=\left(\sin \mathrm{\&theta;}\right)\frac{r_m\&times;n_c}{\left|\right|r_{\mathrm{in}}\&times;n_c\left|\right|}-\left(\cos \mathrm{\&theta;}\right)r_{\mathrm{in}},$

$r_{\mathrm{ref}}=\left(\sin 2\mathrm{\&theta;}\right)\frac{r_{\mathrm{in}}\&times;n_c}{\left|\right|r_{\mathrm{in}}\&times;n_c\left|\right|}-\left(\cos 2\mathrm{\&theta;}\right)r_{\mathrm{in}}.$

2. a kind of many optical-path light-paths of enlargement ratio system of unit that unit according to claim 1 many optical-path light-paths of enlargement ratio astigmatic compensation method constructs with follow-up astigmatic compensation function; It is characterized in that described UMS light path is the BHWC light path, its input and output aperture is positioned over the center of curvature plane homonymy of object lens and field lens; And cut into T-shape to field lens; Distance R=625mm between object lens and field lens, input aperture centre coordinate is (h/2, p; 0), wherein h/2 is input aperture centre distance Y _rThe distance of axle, p is input aperture centre distance X _rThe distance of axle, p=40mm, h=20mm, Δ is the horizontal range of object lens center to self center of curvature, Δ=50mm, light path is counted n=40, and the radius-of-curvature of compensation spherical mirror is r=200mm, beam divergence angle adjustment multiple a=(1: 1)～(3: 1).

3. a kind of many optical-path light-paths of enlargement ratio system of unit that unit according to claim 1 many optical-path light-paths of enlargement ratio astigmatic compensation method constructs with follow-up astigmatic compensation function; It is characterized in that described UMS light path is follow-on White light path; Numerical aperture NA=0.05; Radius-of-curvature is R=750mm, and the radius-of-curvature of compensation spherical mirror is r=200mm, and Δ is the horizontal range of object lens center to self center of curvature; Δ=56mm, beam divergence angle adjustment multiple a=(1: 1) or a=(2: 1).

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