CN1967293A - Manufacturing method of eliminating aberration concave holographic grating - Google Patents

Abstract

The invention discloses a type IV sources aberration concave holographic gratings manufacturing method, in the field of optical instruments and technology. The method is 184mm<rc<224mm, 274mm<rD<234mm, 36< gamma<66, 1<delta<31, of which rc is source point C in the XY plane projection with the O point distance, rD source points in the XY plane D projection and O point distance, OC gamma is the linear projection of the XY plane grating line with the normal rough angle, and delta is in line OD XY linear and planar projection rough grating normal angle. Its beneficial effects lies in that this invention makes type IV concave holographic gratings realization of industrial production, practical, can be achieved by mass production, greatly reducing the cost of production.

Description

The method for making of eliminating aberration concave holographic grating

Technical field

The invention belongs to the optical instrument technical field.

Background technology

At vacuum ultraviolet, particularly grenz ray wave band, all substances all have strong absorption to optical radiation, traditional plane grating spectrograph is owing to introduced collimating mirror and condenser, so there is the supplementary loss that is caused by collimating mirror and condenser, this is unfavorable for the collection efficiency that improves the overall optical spectrometer system.Concave grating is then comparatively superior, because concave grating has the self-focusing characteristic, does not need collimating optical system and Focused Optical system can form spectral line when imaging.Yet there is serious aberration in traditional concave grating, has reduced the spectral line quality of concave grating spectrometer to a great extent, but adopts IV type eliminating aberration concave holographic grating of the present invention just can solve above problem.Use IV type eliminating aberration concave holographic grating can eliminate the aberration of optical system, the size that can dwindle spectral instrument reduces the amount of parts of forming, and improves image quality, resolving power and the measuring accuracy of instrument.

Therefore, IV type eliminating aberration concave holographic grating can be widely used in the spectrometer, and becomes indispensable optical element, and can be used for having unique advantage in the multiwave length spectro device and simple monochromator of visible, ultraviolet region.

Abroad, about theory, design and the making of concave holographic grating is an active research field always, can successfully produce IV type concave holographic grating now according to user's requirement.As the Richardson grating laboratory of the U.S., the Jobin-Yvon company of France, the Hitachi company of Japan, some research institutions such as Zeiss company of Germany.But the price of the concave grating of foreign country is very expensive.

At home, research institutions such as Changchun ray machine institute, China Science ﹠ Technology University's NSRL, exact instrument system of Tsing-Hua University, the digital Optical Co., Ltd of big dimension lattice of Suzhou Soviet Union are carrying out the research of the manufacturing technology of plane holographic grating, but the concave surface holographic grating production of practicability is still blank at home.

Summary of the invention

The objective of the invention is:

A kind of method for making of eliminating aberration concave holographic grating is provided, by calculating the position (distance and the angle that comprise wave source point and grating blank central point) that can draw record spherical wave wave source, can change the size of aberration by the position that changes the spherical wave wave source, and then reach the purpose of anaberration.

Technical scheme of the present invention is:

184mm＜rc＜224mm、

274mm＜rD＜234mm、

36°＜γ＜66°、

1°＜δ＜31°；

Wherein: the rc distance that to be wave source point C order at XY plane projection point and O, the distance that rD wave source point D is ordered at XY plane projection point and O; γ is the angle of straight line OC at XY plane projection straight line and grating blank normal, and δ is the angle of straight line OD at XY plane projection straight line and grating blank normal.

The invention has the beneficial effects as follows:

The present invention makes the production of IV type concave holographic grating realize industrialization, and practicability can realize large batch of making, greatly reduces production cost.

Description of drawings

Fig. 1 is an IV type concave holographic grating geometric parameter synoptic diagram;

Fig. 2 makes IV type concave holographic grating light path synoptic diagram;

Fig. 3 is Seya-Namioka imaging system figure;

Wherein: 1 is Kr ⁺Laser instrument, 2 is plane mirror, and 3 is half-reflecting half mirror, and 4 is plane mirror, 5 is pinhole filter, and 6 is plane mirror, and 7 is pinhole filter, 8 is interference region, and 9 is the grating blank, and angle α and β are that spherical wave passes through the light of grating blank central point and the angle of grating blank normal.

Embodiment

Embodiment 1:

With reference to the coordinate system of figure 1 definition, the summit that makes concave grating is rectangular coordinate system initial point O, and the grating normal is the x axle at O point place, and the plane that definition O point and measuring point light source C, D determine is the xy face, and the xy plane is the plane of symmetry of grating.If grating blank surface is a sphere that radius is R, so, spherical equation can be write as in this coordinate system

(R-ε) ²+ω ²+l ²＝R ² (1)

Wherein (ε, ω l) are the coordinate of any point P on the grating surface.Since ε on the grating black skin, ω, l＜＜R, following formula can be launched into power series, spherical equation then turns to

$\mathrm{\&epsiv;}=\frac{{\mathrm{\&omega;}}^2+l^2}{2R}+\frac{{({\mathrm{\&omega;}}^2+l^2)}^2}{{8R}^3}+\frac{{({\mathrm{\&omega;}}^2+l^2)}^3}{{16R}^5}+\&CenterDot;\&CenterDot;\&CenterDot;---\left(2\right)$

With two wavelength that are used for forming interference fringe is λ ₀The coherent point light source be placed on 2 of C, the D in the xy plane, as shown in Figure 2.If optical path difference＜CP by these 2 any 1 P to the grating black skin 〉-＜DP with these 2 optical path difference＜CO of ordering to O-＜DO difference be λ ₀N doubly, and the 0th bar cutting of regulation grating is by the O point, then the P point is passed through in the n bar cutting of grating, and satisfies following formula

Here

$<\stackrel{\&OverBar;}{\mathrm{CP}}>={[{(x_C-\mathrm{\&epsiv;})}^2+{(y_C-\mathrm{\&omega;})}^2+{(z_C-l)}^2]}^{\frac{1}{2}},$

$<\stackrel{\&OverBar;}{\mathrm{DP}}>={[{(x_D-\mathrm{\&epsiv;})}^2+{(y_D-\mathrm{\&omega;})}^2+{(z_D-l)}^2]}^{\frac{1}{2}},$

$<\stackrel{\&OverBar;}{\mathrm{CO}}>={(r_C^2+z_C^2)}^{\frac{1}{2}},<\stackrel{\&OverBar;}{\mathrm{DO}}>={(r_D^2+z_D^2)}^{\frac{1}{2}},---\left(4\right)$

x _C＝r _Ccosγ，y _C＝r _Csinγ，x _D＝r _Dcosδ，y _D＝r _Dsinδ

Equation (3) is done differential about n (1 is constant), can obtain

${\mathrm{\&lambda;}}_0=\frac{\&PartialD;\mathrm{\&omega;}}{\&PartialD;n}[(\frac{x_D-\mathrm{\&epsiv;}}{<\stackrel{\&OverBar;}{\mathrm{DP}}>}-\frac{x_C-\mathrm{\&epsiv;}}{<\stackrel{\&OverBar;}{\mathrm{CP}}>})\frac{\&PartialD;\mathrm{\&epsiv;}}{\&PartialD;\mathrm{\&omega;}}+\frac{y_D-\mathrm{\&omega;}}{<\stackrel{\&OverBar;}{\mathrm{DP}}>}-\frac{y_C-\mathrm{\&omega;}}{<\stackrel{\&OverBar;}{\mathrm{CP}}>}]---\left(5\right)$

Because, can have in the ω= ε of l=0 place/ ω=0

$\mathrm{\&sigma;}={\mathrm{\&lambda;}}_0{\{{[1+{(z_D/r_D)}^2]}^{-\frac{1}{2}}\sin \mathrm{\&delta;}-{[1+{(z_C/r_C)}^2]}^{-\frac{1}{2}}\sin \mathrm{\&gamma;}\}}^{-1}$

2 of measuring point light source C, D are positioned on the xy plane in the reality, so following formula can be write as

σ＝λ/(sinδ-sinγ)，δ＞γ (6)

Make A (x, y, the z) incidence point when using grating, B (x ', y ', z ') for light through the eye point behind the grating, and be that wavelength is the inferior light of m level of λ through P point diffraction.

For light APB, iconal F is:

F＝< AP>+< PB>+nmλ (7)

Here

$<\stackrel{\&OverBar;}{\mathrm{AP}}>={[{(x-\mathrm{\&epsiv;})}^2+{(y-\mathrm{\&omega;})}^2+{(z-l)}^2]}^{\frac{1}{2}},$

$<\stackrel{\&OverBar;}{\mathrm{PB}}>={[{(x^{\&prime;}-\mathrm{\&epsiv;})}^2+{(y^{\&prime;}-\mathrm{\&omega;})}^2+{(z^{\&prime;}-l)}^2]}^{\frac{1}{2}},---\left(8\right)$

x＝rcosα，y＝rsinα，x′＝r′cosβ，y′＝r′sinβ.

Wherein, α, β are respectively incident angle and the angle of diffraction that records under the xy plane.It is not only relevant with the position of 2 of A, B to draw iconal F to (3) formula (7) formula that is updated to, but also relevant with the position of recording light source C, D.(2), (3), (8) formula are updated in (7) formula, and are launched into power series, can obtain

$F=F_{000}+\mathrm{\&omega;}{F}_{100}+l{F}_{011}+\frac{1}{2}{\mathrm{\&omega;}}^2{F}_{200}+\frac{1}{2}{l}^2{F}_{020}+\frac{1}{2}{\mathrm{\&omega;}}^3{F}_{300}+\frac{1}{2}\mathrm{\&omega;}{l}^2{F}_{120}---\left(9\right)$

$\mathrm{\&omega;l}{F}_{111}+\frac{1}{8}{\mathrm{\&omega;}}^4{F}_{400}+\frac{1}{4}{\mathrm{\&omega;}}^2{l}^2{F}_{300}+\frac{1}{8}{l}^4{F}_{040}+\&CenterDot;\&CenterDot;\&CenterDot;$

Every coefficient F in the formula _IjkSubscript (i, j, k) and ω ⁱ, l ^j, z ^kThe index correspondence.F _IjkExpression formula be

$F_{\mathrm{ijk}}=M_{\mathrm{ijk}}+\frac{\mathrm{m\&lambda;}}{{\mathrm{\&lambda;}}_0}{H}_{\mathrm{ijk}}---\left(10\right)$

Here, last the structural parameters by imaging system determine, back one relevant with holographic recording parameter.Each dominant term coefficient has following meaning: F in the formula (9) ₂₀₀(out of focus item), F ₀₂₀(astigmatism item), F ₁₂₀(astigmatism coma item), F ₃₀₀(meridian coma item), F ₄₀₀, F ₂₂₀, F ₀₄₀(various spherical aberration item).

M _IjkAnd H _IjkFor (i, j, k)=(200), and (020), (120) can be expressed as when (300)

M _ijk＝f(ρ，α)+f(ρ′，β)，

H _ijk＝f(ρ _C，γ)-f(ρ _D，δ)，

Here

ρ＝R/r，ρ′＝R/r′，ρ _C＝?R/r _C，ρ _D＝R/r _D。

According to the Fermat principle, when $\frac{\&PartialD;F}{\&PartialD;\mathrm{\&omega;}}=0$ With $\frac{\&PartialD;F}{\&PartialD;l}=0$ The time, aberration is zero.In fact this condition is impossible strictly to realize, but as if the high-order term in these two partial derivatives of ignoring iconal, and its main several are equalled zero or minimalization, the Fermat principle just can be satisfied approx.

Fig. 3 is the Seya-Namioka imaging system, and the concrete geometry parameter that is used to shelve the Seya-Namioka imaging system of IV type concave holographic grating is

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="A20061001660900111.png"\; state="\{\{state\}\}">r</figure-callout>}}_0,{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="A20061001660900111.png"\; state="\{\{state\}\}">r</figure-callout>}}_0^{\&prime;}=\mathrm{const}\\ 2K={\mathrm{\&alpha;}}_0-{\mathrm{\&beta;}}_0=\mathrm{const}\\ {\mathrm{\&alpha;}}_0=\mathrm{\&theta;}+K\\ {\mathrm{\&beta;}}_0=\mathrm{\&theta;}-K\end{array}\right.---\left(11\right)$

In the formula, r ₀, r ₀' be respectively distance A 0O and B0O; θ is the corner of grating normal to the angular bisector at 2K angle.

In the Seya-Namioka imaging system, grating equation is

2σcos?Ksinθ＝mλ (12)

When using concave grating, aberration minimalization in the concave grating service band that we can only make defocusing amount and wish to eliminate.For this reason, the integration minimization below the order

$I_{\mathrm{ijk}}={\&Integral;}_{{\mathrm{\&theta;}}_1\left({\mathrm{\&lambda;}}_1\right)}^{{\mathrm{\&theta;}}_2\left({\mathrm{\&lambda;}}_2\right)}{F}_{\mathrm{ijk}}^2\mathrm{d\&theta;}=\min \&CenterDot;---\left(13\right)$

θ in the formula ₁And θ ₂Be that concave grating is corresponding to service band (λ ₁≤ λ≤λ ₂) initial and stop corner.

Order $A_{\mathrm{ijk}}=H_{\mathrm{ijk}}/(\sin \mathrm{\&delta;}-\sin \mathrm{\&gamma;})=\frac{\mathrm{\&sigma;}}{{\mathrm{\&lambda;}}_0}{H}_{\mathrm{ijk}}---\left(14\right)$

In general, the astigmatism of Seya-Namioka imaging system is very big, must choose reasonable geometric parameter r during use ₀, r ₀', K and A _Ijk, A here _IjkWhen being the recording holographic grating and the parameter of introducing, it is the position that is used for limiting measuring point.According to F _IjkMeaning, if get (ijk)=(200), this up-to-date style (13) is

$I_{200}={\&Integral;}_{{\mathrm{\&theta;}}_1\left({\mathrm{\&lambda;}}_1\right)}^{{\mathrm{\&theta;}}_2\left({\mathrm{\&lambda;}}_2\right)}{F}_{200}^2\mathrm{d\&theta;}=\min ---\left(15\right)$

Like this, the Seya-Namioka imaging system is at θ ₁(λ ₁)≤θ (λ)≤θ ₂(λ ₂) all will satisfy the horizontal focusing condition preferably in the scope.Be equivalent to formula (13), promptly take off the group that establishes an equation:

$\left\{\begin{array}{c}{\&PartialD;I}_{200}/\&PartialD;\mathrm{\&rho;}=0\\ {\&PartialD;I}_{200}/{\&PartialD;\mathrm{\&rho;}}^{\&prime;}=0\\ {\&PartialD;I}_{200}/\&PartialD;K=0\\ {\&PartialD;I}_{200}/{\&PartialD;A}_{200}=0\end{array}\right.---\left(16\right)$

Can try to achieve structure parameter ρ, ρ ', K and the A of Seya-Namioka imaging system ₂₀₀

After ρ, ρ ' and K were selected, each integration of formula (13) was A _IjkFunction.Therefore can be by  I _Ijk/  A _Ijk=0 condition is tried to achieve the A that satisfies formula (15) _IjkSubstitution formula again (14) just can be determined the position of recording light source, thereby makes certain aberration minimization.In the reality, mainly be that astigmatism item [(ijk)=(020)], coma item [(ijk)=(300)] or coma item [(ijk)=(300), (120)] are minimized.

The anaberration condition of decision holographic recording parameter is divided coma correction type (f ₂₀₀, f ₃₀₀, f ₁₂₀) and astigmatic correction type (f ₂₀₀, f ₃₀₀, f ₀₂₀), respectively with following two formulas statement:

$\left\{\begin{array}{c}\sin \mathrm{\&delta;}-\sin \mathrm{\&gamma;}={\mathrm{\&lambda;}}_0/\mathrm{\&sigma;}\\ f_{200}({\mathrm{\&rho;}}_C,\mathrm{\&gamma;})-f_{200}({\mathrm{\&rho;}}_D,\mathrm{\&delta;})=({\mathrm{\&lambda;}}_0/\mathrm{\&sigma;})A_{200}\\ f_{300}({\mathrm{\&rho;}}_C,\mathrm{\&gamma;})-f_{300}({\mathrm{\&rho;}}_D,\mathrm{\&delta;})=({\mathrm{\&lambda;}}_0/\mathrm{\&sigma;})A_{300}\\ f_{120}({\mathrm{\&rho;}}_C,\mathrm{\&gamma;})-f_{120}({\mathrm{\&rho;}}_D,\mathrm{\&delta;})=({\mathrm{\&lambda;}}_0/\mathrm{\&sigma;})A_{120}\end{array}\right.---\left(17\right)$

$\left\{\begin{array}{c}\sin \mathrm{\&delta;}-\sin \mathrm{\&gamma;}={\mathrm{\&lambda;}}_0/\mathrm{\&sigma;}\\ f_{200}({\mathrm{\&rho;}}_C,\mathrm{\&gamma;})-f_{200}({\mathrm{\&rho;}}_D,\mathrm{\&delta;})=({\mathrm{\&lambda;}}_0/\mathrm{\&sigma;})A_{200}\\ f_{300}({\mathrm{\&rho;}}_C,\mathrm{\&gamma;})-f_{300}({\mathrm{\&rho;}}_D,\mathrm{\&delta;})=({\mathrm{\&lambda;}}_0/\mathrm{\&sigma;})A_{300}\\ f_{020}({\mathrm{\&rho;}}_C,\mathrm{\&gamma;})-f_{020}({\mathrm{\&rho;}}_D,\mathrm{\&delta;})=({\mathrm{\&lambda;}}_0/\mathrm{\&sigma;})A_{020}\end{array}\right.---\left(18\right)$

Adopt the computer numerical method to find the solution, can draw the concrete parameter of record IV type concave holographic grating.

Technical essential is: when the monochromatic spherical wave of two bundles meets with certain angle, the zone of intersecting at them will form interference field, produce light and dark interference fringe, and this interference field is exactly the exposure region that we will use.Be placed in the interference field if will scribble the blank of photoresist, will produce cutting because of light and dark interference fringe on the blank surface so.By calculating the position (distance and the angle that comprise wave source point and grating blank central point) that can draw record spherical wave wave source, theoretical analysis and result of calculation show, can change the size of aberration by the position that changes the spherical wave wave source, and then reach the purpose of anaberration.

Send a branch of light by ray laser bundle 1, through plane mirror 2, be divided into two-beam behind the half-reflecting half mirror 3, this two-beam passes through plane mirror 4,6 and pinhole filter 5,7 respectively, laser beam is through forming two bundle spherical waves behind the pinhole filter, this two bundles spherical wave intersects at a certain angle, forms interference region 8, and this interference region is exactly the exposure region that we will use.The concave grating blank 9 that scribbles photoresist is placed in the exposure region with certain angle, chooses the suitable time shutter according to light intensity magnitude, the back just can obtain the grating cutting on the grating blank through developing.Pass through ion beam etching again, just can obtain IV type concave holographic grating.It is the Kr of 431.1nm that laser wavelength of incidence is selected in this experiment for use ⁺Laser instrument, by changing the IV type concave holographic grating that α and β angle obtain different grating constants, what we made in the experiment is the grating of 1200 lines per millimeters.

Claims (1)

1, a kind of method for making of IV type eliminating aberration concave holographic grating, its method for making is:

184mm＜rc＜224mm、

274mm＜rD＜234mm、

36＜γ＜66、

1＜δ＜31；

Wherein: the rc distance that to be wave source point C order at XY plane projection point and O, the distance that rD wave source point D is ordered at XY plane projection point and O; γ is the angle of straight line OC at XY plane projection straight line and grating blank normal, and δ is the angle of straight line OD at XY plane projection straight line and grating blank normal.

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