CN104777529B - A kind of design preparation method compensating the optical anti-reflection multilayer film of simple lens spherical aberration - Google Patents

Abstract

The invention discloses a kind of design preparation method compensating the optical anti-reflection multilayer film of simple lens spherical aberration, comprise: 1) calculate linearly polarized light emergent pupil face place wavefront difference a that spherical aberration produces after simple lens, set up the funtcional relationship between wavefront difference a and incident angle, divided by 2 π remainder numbers, wavefront difference b is obtained to wavefront difference a negate; 2) value in the several interval of wavefront difference b is averaged respectively, obtain the wavefront difference c of discrete distribution; 3) for several interval, the corresponding film system of optimal design respectively.Take the wavefront difference c under corresponding incident angle as the optimization aim of the optical anti-reflection film design in this interval, carry out the optimal design of optical anti-reflection film; 4) several optical anti-reflection multilayer films of design gained are spliced from small to large by incident angle, obtain the optical anti-reflection film compressing simple lens spherical aberration.

Description

A kind of design preparation method compensating the optical anti-reflection multilayer film of simple lens spherical aberration

Technical field

The present invention relates to optical multilayer field, be specifically related to a kind of design preparation method compensating the optical anti-reflection multilayer film of simple lens spherical aberration.

Background technology

Along with immersion lithography, biological microscopy etc. are in the development of interior optical system with high NA, also bring challenge to the design of components and parts relevant to it and processing and manufacturing, many key parameters are all never relate in conventional objective design.In this type of optical system with high NA worked under Single wavelength, the spherical aberration of lens is obvious, system focal beam spot can be made to form middle bright limb speck fuzzy gradually, thus affect image quality.Therefore, must be corrected, otherwise directly can be affected operating accuracy and the work efficiency of optical system.

Under normal circumstances, adopt the incompatible elimination spherical aberration of lens combination, because spherical aberration that is convex, concavees lens is contrary, the meniscus gummed can matching different materials gets up to eliminate.But this lens combination eliminates the mode of spherical aberration, adds extra element, add the cost of optical system in optical system, also add difficulty for later stage of optical system debugs.

Publication number is disclose a kind of optical aberration compensating lens in the patent of invention " optical aberration compensating lens " of CN1664622A (application number is 200410006531.8), comprise a lens body and multiple light filter film, wherein, lens body has a light entrance face, an exit facet and an optical axis, and light entrance face and/or light-emitting face are made up of multiple discontinuous block.Be divided into ring-type block, sector block, the polygon block of multiple different size at the plane of incidence/of lens or exit facet, multiple light filter film be configured at respectively these blocks of lens body, carry out aberration compensation.This mode will carry out lithography to lens on the one hand, also will carry out the preparation of optical thin film in addition on the one hand at uneven lens surface, all higher to the requirement of lens processing and film preparation.

Summary of the invention

The present invention is directed in conventional lenses spherical aberration correction procedure and can introduce extra lens, cause the technical matters such as cost increase, the increase of optical system alignment difficulty, provide a kind of when not changing lens face type, not increasing additional optical elements, realize the method that simple lens spherical aberration is compressed.By to the analysis through signal-lens emerging wavefront difference, propose the optical anti-reflection multilayer film Phase design method of compression simple lens spherical aberration, utilize the bit phase delay of film to compensate compression to wavefront variation.Thus realize when without additional optics, to compensation and the compression of signal-lens spherical aberration excellence.

Compensate a design preparation method for the optical anti-reflection multilayer film of simple lens spherical aberration, it is characterized in that, comprise the following steps:

1) according to the signal-lens plane of incidence and exit facet characteristic, the coefficient of spherical aberration item in the zernike polynomial of light field wavefront difference after simple lens is calculated;

2) step 1 is utilized) the middle coefficient calculating spherical aberration item in the zernike polynomial of gained, calculate linearly polarized light emergent pupil face place wavefront difference that spherical aberration produces after simple lens, getting this wavefront difference corresponding to a series of values on footpath, pole, simple lens emergent pupil face is wavefront difference a;

Utilize the signal-lens plane of incidence and exit facet characteristic (i.e. signal-lens parameter), calculate directional light incident time, the function that the incident angle of the simple lens plane of incidence converts with footpath, emergent pupil pole;

Utilize footpath, emergent pupil pole, set up the funtcional relationship between wavefront difference a and incident angle;

3) by wavefront difference a negate, and divided by 2 π and remainder number, obtain wavefront difference b, wavefront difference b is divided into several interval according to different ranges of incidence angles, obtains the wavefront difference b in several interval;

Value in the several interval of wavefront difference b is averaged respectively, obtains the wavefront difference c of discrete distribution;

4) be initial configuration with the anti-reflection film film adopting the second index layer and first refractive rate layer optics to replace, evaluation function is F=(I × D × C-T)/N, I=1 is the intensity of light source, D=1 is detector efficiency, C is that the position calculating gained under corresponding incident angle is worth mutually, T is that the target bit under corresponding ranges of incidence angles is worth mutually, and N=1 is normalized factor;

In each interval of wavefront difference c, be that the target bit of the optical anti-reflection film Film Design in this interval is worth mutually with the wavefront difference c value in this interval, N=1 is normalized factor, evaluation function F is made to be minimised as design object, obtain each layer thickness and the periodicity of the second index layer and first refractive rate layer in different interval interior each optical anti-reflection film, each optical anti-reflection film under namely different ranges of incidence angles;

5) on simple lens, prepare each optical anti-reflection film according to different ranges of incidence angles, be compensated the optical anti-reflection multilayer film of simple lens spherical aberration.

Step 1) in, in described zernike polynomial, the coefficient (value) of spherical aberration item can be calculated by business softwares such as ZEMAX, can calculate at a particular wavelength, as under operation wavelength 587.6nm.In the business softwares such as ZEMAX, input the signal-lens plane of incidence and exit facet characteristic (i.e. signal-lens parameter) and operation wavelength, the coefficient of spherical aberration item in zernike polynomial can be obtained.

Described simple lens is concavees lens or convex lens.

Step 2) in, with signal-lens optical axis for x-axis, with the intersection point of signal-lens optical axis and the plane of incidence for initial point, set up xy axle rectangular coordinate system;

Utilize step 1) the middle coefficient calculating spherical aberration item in the zernike polynomial of gained, calculate linearly polarized light emergent pupil face place wavefront difference that spherical aberration produces after simple lens, getting this wavefront difference corresponding to a series of values on footpath, pole, simple lens emergent pupil face is wavefront difference a;

$a=R\×\sqrt{5}(6{\mathrm{\ρ}}^4-6{\mathrm{\ρ}}^2+1)---\left(1\right)$

In formula, ρ is footpath, polar pole, simple lens emergent pupil face, and R is the coefficient of spherical aberration item in zernike polynomial;

The wavefront difference in simple lens y-axis direction represents the variation tendency of the wavefront difference in whole emergent pupil face, namely

$a=R\×\sqrt{5}(6y^4-6y^2+1)---\left(2\right)$

The incident angle A of the simple lens plane of incidence and the funtcional relationship of y-axis:

$A=\frac{\mathrm{\π}}{2}-\arctan \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)---\left(3\right)$

The functional relation of x and y is set up by the signal-lens plane of incidence:

$x=\frac{y^2}{8.1+\sqrt{{8.1}^2-0.46y^2}}---\left(4\right)$

By (2), (3), (4) formula, set up the funtcional relationship of incident angle A and wavefront difference a.

Step 3) in, described several intervals are 3 ~ 10, are determined with the trend of entrance pupil change in radius by wavefront difference b.

Wavefront difference b is divided into several interval according to different ranges of incidence angles, as got the mean value of wavefront difference c within the scope of incident angle 0 ~ 25 degree, be first interval, the mean value of wavefront difference c is got within the scope of incident angle 25 ~ 45 degree, be second interval, within the scope of incident angle 45 ~ 50 degree, get the mean value of wavefront difference c, be the 3rd interval.In each interval, wavefront difference c is constant.

Step 4) in, an interval ranges of incidence angles of corresponding, different interval corresponding different ranges of incidence angles, an optical anti-reflection film is obtained through optimization in an interval, obtain different interval different optical anti-reflective film, the different optical anti-reflective film under namely different ranges of incidence angles.

As preferably, described first refractive rate layer, as low-index layer, is SiO ₂layer, Al ₂o ₃layer or MgF ₂layer.

As preferably, the second described index layer, as high refractive index layer, is TiO ₂, HfO ₂or LaF ₃, above-mentioned material is high-index material, is the material of the ground floor of antireflective optical multilayer film.

Described subregion is optimized, the piecewise function relation of wavefront difference c and incident angle, for different incident angles, select corresponding wavefront difference c to be the additional optimizations condition of the optical anti-reflection film design in this interval, obtain for the second layer refractive index of the optical anti-reflection multilayer film compressing simple lens spherical aberration in different ranges of incidence angles, the thickness optimization value of ground floor refractive index and periodicity.

The thickness optimization of the second described index layer and first refractive rate layer can adopt the design of TFCalc business software to obtain.The initial film system of anti-reflection film film system is alternately made up of the second index layer (high refractive index layer) and first refractive rate layer (low-index layer), can adopt (HL) ^ ³for initial film system (see " contemporary optics thin film technique " chapter 3, optical thin film system, Tang Jinfa, Gu Peifu, Liu Xu, Li Haifeng work, publishing house of Zhejiang University November in 2006 the 1st edition).Initial film system can select high refractive index layer H to be TiO further ₂, thickness is 56.1nm, and low-index layer L is SiO ₂, thickness is 100.6nm, and periodicity is 3.In optimizing process, evaluation function is F=(I × D × C-T)/N, I=1 is the intensity of light source, D=1 is detector efficiency, and C is the reflectivity calculating gained, and T is reflectivity desired value (i.e. specified wavelength place, reflectivity is 0), N=1 is normalized factor.In optimizing process, for different incident angles, corresponding wavefront difference 4 is selected to be the position phase optimal conditions of the optical anti-reflection film design in this interval, changeable parameter is the second index layer, each layer thickness of first refractive rate layer and the number of plies, make evaluation function be minimised as design object, obtain the thickness optimization value of the second index layer and first refractive rate layer and the number of plies after optimizing.

Step 5) in, on simple lens, prepare each optical anti-reflection film according to different ranges of incidence angles, be compensated the optical anti-reflection multilayer film of simple lens spherical aberration.Therefore, the diverse location on the plane of incidence on simple lens, the difference of ranges of incidence angles, prepares different optical anti-reflection films, is stitched together.Namely several optical anti-reflection multilayer films of gained splice from small to large by incident angle, are compensated the optical anti-reflection multilayer film of simple lens spherical aberration.

Relative to prior art, the present invention has following useful technique effect:

The present invention, by carrying out analytical calculation to the wavefront difference that simple lens spherical aberration produces, obtains optimizing constraint condition mutually for the optical anti-reflection film position in different incidence angles interval.In corresponding incident angle interval, the initial configuration of constraint condition to optical anti-reflection film is utilized to be optimized design respectively.Finally several optical anti-reflection multilayer films of design gained are spliced from small to large by incident angle, obtain the optical anti-reflection film compressing simple lens spherical aberration.The wavefront difference that the present invention utilizes optical anti-reflection film position to produce mutually compensates the wavefront difference that simple lens spherical aberration produces.While utilizing optical anti-reflection film to improve the transmitance of lens, also have compressed signal-lens spherical aberration when not introducing additional optical elements, thus simplify optical system structure, improve optical system integrated level, reduce the resetting difficulty of optical system, reduce the cost of optical system.

Accompanying drawing explanation

Fig. 1 is for directional light is by the wavefront difference after simple lens caused by radial direction spherical aberration, comprise incident directional light 1, simple lens 2, divide other wavefront difference a along direction, footpath, pole, emergent pupil face, and after the simple lens applying ordinary optical antireflection multilayer film, be wavefront difference d by signal-lens light field wavefront;

Fig. 2 is that the position of optical anti-reflection film initial configuration accompanies the curve of angle change;

Fig. 3 is the relation schematic diagram of simple lens surface incident angle and lens parameter;

Fig. 4 is the funtcional relationship of lens surface incident angle A and lens wavefront difference a;

Fig. 5 is the funtcional relationship of incident angle and wavefront difference b, and wherein wavefront difference b is by wavefront difference a negate, gained divided by 2 π and after remainder number;

Fig. 6 is the funtcional relationship of incident angle and wavefront difference c, and wavefront difference c is three intervals 3,4 to wavefront difference b, and the value of 5 li is averaged gained respectively;

Fig. 7 is incident angle and the funtcional relationship of the optical anti-reflection film position phase of compression simple lens spherical aberration;

Fig. 8 is the wavefront difference of the optical anti-reflection film rear lens applying compression simple lens spherical aberration.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described, but the present invention is not limited to this.

As shown in Figure 1, directional light 1, by the wavefront difference a after simple lens 2 caused by radial direction spherical aberration, comprises the wavefront difference a of incident directional light 1, simple lens 2 and footpath, pole, the emergent pupil face directional spreding along simple lens 2.Directional light 1 is by after simple lens 2, and the spherical aberration of simple lens 2 can have an impact to the wavefront of plane wave, and induction wavefront difference, changes over the shape of wavefront difference a by the plane wave of the directional light 1 of incidence.The change of this wavefront can cause the decline of optics into focus characteristic, should be revised in the use of simple lens 2.

The existing common optical anti-reflection film being applied to Single wavelength optical system for this type of comprises high refractive index layer and low-index layer, and high refractive index layer and low-index layer are alternately arranged, for the film system of conventional optical thin film, its thickness of every layer has specific works wavelength to determine.This kind of optical anti-reflection film only can promote the transmitance of lens to some extent, and can not have compensation, correcting to the wavefront difference of lens.

Common optical anti-reflection film design process is usually as follows: with (HL) ^ ³for initial configuration, (the second index layer and high refractive index layer H are TiO ₂, thickness is 56.1nm, and first refractive rate layer and low-index layer L are SiO ₂, thickness is 100.6nm, and high refractive index layer H and low-index layer L is alternately once a cycle, and periodicity is 3).In optimizing process, evaluation function is F=(I × D × C-T)/N, I=1 is the intensity of light source, D=1 is detector efficiency, and C is that the position calculating gained is worth mutually, and T is that reflectivity target is (namely under operation wavelength 587.6nm, reflectivity is 0), N=1 is normalized factor.In optimizing process, changeable parameter is the second index layer, each layer thickness of first refractive rate layer and periodicity, make evaluation function be minimised as design object, obtain the thickness optimization value of the second index layer and first refractive rate layer and the periodicity after optimizing.Result after optimization is as shown in table 1, and wherein, H represents the material TiO of high refractive index layer ₂, L represents the materials A l of low-index layer ₂o ₃specifically as ground floor in table 1 starts alternately, finally obtain existing optical anti-reflection multilayer film, this optical anti-reflection multilayer film (abbreviation film) position accompany angle change curve as shown in Figure 2, horizontal ordinate is the incident angle (unit: degree) of optical anti-reflection multi-layer film surface, ordinate is that the average bit of optical anti-reflection multilayer film s, p light is worth mutually, and average bit is worth mutually and is the impact of optical anti-reflection multilayer film on light field wavefront.Therefore by after the simple lens 2 that applies ordinary optical antireflection multilayer film, the wavefront difference of light field can't be compensated, and light field wavefront is now wavefront difference d (shown in Fig. 1), basically identical with wavefront difference a.

Table 1

Number of plies #	Material	Thickness
			1	H	78.79
2	L	55.29
			3	H	32.43
4	L	62.05
			5	H	79.37
6	L	135.08

In order to solve the problem, compensate the spherical aberration of simple lens 2.The present invention proposes to design mutually the position of optical anti-reflection multilayer film, utilizes the phasic difference caused by phase compensation simple lens spherical aberration of optical anti-reflection multilayer film.By obtaining the wavefront being separated into several intervals to wavefront difference a negate, divided by 2 π after remainder number, and in these several intervals, wavefront value to be averaged respectively.Position phase optimization aim using these values as optical anti-reflection multilayer film s, p light under corresponding incident angle, in corresponding interval, in his-and-hers watches 1, optical anti-reflection multilayer film carries out optimal design again respectively.Obtain the optical anti-reflection film system in several incident angle intervals, finally according to the variation tendency of incident angle, the antireflective film in these several intervals is merged, obtain the optical anti-reflection multilayer membrane system (namely compressing the optical anti-reflection multilayer film of simple lens spherical aberration) compressing simple lens spherical aberration.

Embodiment 1

Be further described below in conjunction with the optical anti-reflection multilayer film of embodiment to the compression simple lens spherical aberration that the present invention proposes, but the present invention is not limited to this.

As shown in Figure 1, Figure 3, directional light 1 is by after simple lens 2, and simple lens 2 can produce spherical aberration, causes the change of emergent pupil face light field wavefront, produces wavefront difference a.Simple lens shown in Fig. 32, first face is aspheric surface, and second face is plane, and first face and second face are 7mm in the distance of optical axis direction.First face causes the spherical aberration of simple lens 2, and the coefficient of zernike polynomial spherical aberration item is changed, and in Fig. 3, this coefficient signal-lens can use the business softwares such as ZEMAX to calculate, and obtains coefficients R=2.4038 of zernike polynomial spherical aberration item.This coefficient is multiplied by the spherical aberration item in zernike polynomial, just can obtain the wavefront difference a because simple lens 2 spherical aberration produces,

$a=R\×\sqrt{5}(6{\mathrm{\ρ}}^4-6{\mathrm{\ρ}}^2+1)---\left(1\right)$

In formula, ρ is footpath, polar pole, emergent pupil face, as shown in Figure 3.

Because this wavefront difference a is rotational symmetric centered by signal-lens optical axis (x-axis in Fig. 3), therefore the wavefront difference in lens y-axis direction just can represent the variation tendency of the wavefront difference in whole emergent pupil face, namely

$a=R\×\sqrt{5}(6y^4-6y^2+1)---\left(2\right)$

Shown in Fig. 3, the funtcional relationship of the surperficial incident angle A of simple lens first and y-axis can be specified: the incident angle of light in first face can be with function representation:

$A=\frac{\mathrm{\π}}{2}-\arctan \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)---\left(3\right)$

Wherein, the functional relation of x and y can be set up by the function expression in first face:

$x=\frac{y^2}{8.1+\sqrt{{8.1}^2-0.46y^2}}---\left(4\right)$

By (2), (3), (4) formula, the funtcional relationship of incident angle A and wavefront difference a can be set up, as shown in Figure 4.

By wavefront difference a negate, obtain wavefront difference b divided by 2 π after remainder number, as shown in Figure 5, obviously can find out that wavefront difference b is divided into interval 3, interval 4 and interval 5, three intervals.

Three intervals (namely interval 3, interval 4 and interval 5) the inner value of wavefront difference b is averaged respectively, obtains the interval 6 of wavefront difference c, interval 7 and interval 8 three discontinuous intervals, as shown in Figure 6.

Be initial configuration with the optical anti-reflection film of table 1, in further process of optimization, evaluation function is F=(I × D × C-T)/N, I=1 is the intensity of light source, D=1 is detector efficiency, C is that the position calculating gained under corresponding incident angle is worth mutually, and T is that the target bit under corresponding incident angle is worth (i.e. optimization aim) mutually, and N=1 is normalized factor.In optimizing process, for interval 6, interval 7 and interval 8 three intervals, respectively optimal design three film systems.In each interval, take the wavefront difference under corresponding incident angle as the optimization aim (i.e. T) of the optical anti-reflection film design in this interval, changeable parameter is the second index layer, each layer thickness of first refractive rate layer and periodicity, make evaluation function be minimised as design object, obtain thickness optimization value and the number of plies of the second index layer and first refractive rate layer.Optimizing process can adopt TFCalc business software to realize.The structure of three antireflection multilayer films of final design is as table 2, and table 3, shown in table 4, is applied to interval 6, interval 7 and interval 8, i.e. table 2 corresponding interval 6, table 3 corresponding interval 7, table 4 corresponding interval 8 respectively.Spliced from small to large by incident angle by these three optical anti-reflection multilayer films, can be compensated the optical anti-reflection film of above-mentioned simple lens spherical aberration, its phase as shown in Figure 7.

Table 2

Number of plies #	Material	Thickness
			1	H	8.50
2	L	37.70
			3	H	106.01
4	L	55.75
			5	H	9.55

Table 3

Number of plies #	Material	Thickness
			1	H	22.68
2	L	23.43
			3	H	114.49
4	L	13.08
			5	H	104.63
6	L	61.18
			7	H	13.46

Table 4

Number of plies #	Material	Thickness
			1	H	11.69

2	L	54.86
			3	H	122.86 6 -->
4	L	79.38
			5	H	3.88

Be added compensating the wavefront difference that in the position phase of the optical anti-reflection film of simple lens spherical aberration and Fig. 4, simple lens spherical aberration produces in Fig. 7, the lens wavefront difference that can be applied after compensating the optical anti-reflection film of simple lens spherical aberration, as shown in Figure 8.Comparison diagram 4 and Fig. 8, can it is evident that, the optical anti-reflection film that compensates simple lens spherical aberration is to the amplitude compression of wavefront difference a nearly 43%, and the variation tendency of remaining wavefront difference will be far smaller than the variation tendency of wavefront difference a, the optical anti-reflection multilayer film compensating simple lens spherical aberration has excellent compression really to simple lens spherical aberration.

Claims (5)

1. compensate a design preparation method for the optical anti-reflection multilayer film of simple lens spherical aberration, it is characterized in that, comprise the following steps:

1) according to the signal-lens plane of incidence and exit facet characteristic, the coefficient of spherical aberration item in the zernike polynomial of light field wavefront difference after simple lens is calculated;

2) step 1 is utilized) the middle coefficient calculating spherical aberration item in the zernike polynomial of gained, calculate linearly polarized light emergent pupil face place wavefront difference that spherical aberration produces after simple lens, getting this wavefront difference corresponding to a series of values on footpath, pole, simple lens emergent pupil face is wavefront difference a;

Utilize the signal-lens plane of incidence and exit facet characteristic, calculate directional light incident time, the function that the incident angle of the simple lens plane of incidence converts with footpath, emergent pupil pole;

Utilize footpath, emergent pupil pole, set up the funtcional relationship between wavefront difference a and incident angle;

3) by wavefront difference a negate, and divided by 2 π and remainder number, obtain wavefront difference b, wavefront difference b is divided into several interval according to different ranges of incidence angles, obtains the wavefront difference b in several interval;

Value in the several interval of wavefront difference b is averaged respectively, obtains the wavefront difference c of discrete distribution;

4) the anti-reflection film film replaced with the second index layer and first refractive rate layer is initial configuration, evaluation function is F=(I × D × C-T)/N, I=1 is the intensity of light source, D=1 is detector efficiency, C is that the position calculating gained under corresponding incident angle is worth mutually, T is that the target bit under corresponding ranges of incidence angles is worth mutually, and N=1 is normalized factor;

In each interval of wavefront difference c, be that the target bit of the optical anti-reflection film Film Design in this interval is worth mutually with the wavefront difference c value in this interval, evaluation function F is made to be minimised as design object, obtain each layer thickness and the periodicity of the second index layer and first refractive rate layer in different interval interior each optical anti-reflection film, each optical anti-reflection film under namely different ranges of incidence angles;

5) on simple lens, prepare each optical anti-reflection film according to different ranges of incidence angles, splicing is compensated the optical anti-reflection multilayer film of simple lens spherical aberration.

2. the design preparation method of the optical anti-reflection multilayer film of compensation simple lens spherical aberration according to claim 1, is characterized in that, step 1) in, described simple lens is concavees lens or convex lens.

3. the design preparation method of the optical anti-reflection multilayer film of compensation simple lens spherical aberration according to claim 1, is characterized in that, step 3) in, described several intervals are 3 ~ 10.

4. the design preparation method of the optical anti-reflection multilayer film of compensation simple lens spherical aberration according to claim 1, is characterized in that, step 4) in, described first refractive rate layer is SiO ₂layer, Al ₂o ₃layer or MgF ₂layer.

5. the design preparation method of the optical anti-reflection multilayer film of compensation simple lens spherical aberration according to claim 1, is characterized in that, step 4) in, the second described index layer is TiO ₂layer, HfO ₂layer or LaF ₃layer.