CN101813797A - Optimal design method of multilayer diffraction optical element - Google Patents

Abstract

The invention relates to an optimal design method of a multilayer diffraction optical element, which belongs to the technical field of optical design. The optimal design is not realized in the prior art. The method comprises the following steps of: (1) optimally selecting an optical material of the multilayer diffraction optical element according to a surface microstructure height formula of the multilayer diffraction optical element; (2) determining the bandwidth integration average diffraction efficiency distribution by using different design wavelength combinations in the entire working waveband; (3) determining the greatest bandwidth integration average diffraction efficiency and the relative design wavelength in the entire working waveband; and (4) substituting the design wavelength corresponding to the greatest bandwidth integration average diffraction efficiency into the surface microstructure height formula of the multilayer diffraction optical element, and calculating out the optimal surface microstructure height and the optimal design wavelength of the multilayer diffraction optical element. The method is used for designing the multilayer diffraction optical element used for a wide-waveband imaging optical system, and maximizes the bandwidth integration average diffraction efficiency of the multilayer diffraction optical element.

Description

The Optimization Design of multilayer diffraction optical element

Technical field

The present invention relates to a kind of Optimization Design of multilayer diffraction optical element, be used for the multilayer diffraction optical element design of broadband imaging optical system, this method can realize the maximization of bandwidth integral mean diffraction efficiency, the quantification optimal design of multilayer diffraction optical element, can improve the image quality of the folding/hybrid optical system that spreads out that contains multilayer diffraction optical element, belong to the optical design technical field.

Background technology

Along with the development of Optical manufacture technology, diffraction optical element has been created an independently branch in contemporary optics, has brought revolutionary variation for traditional optical design theory and manufacturing process.Diffraction optical element can be used for various image defects such as correcting chromatic aberration, aberration, brings more design freedom and broad material washability to optical design, thereby can realize special optical function.Rolling over/spreading out in the hybrid optical system design process, because the diffraction efficiency of individual layer diffraction optical element sharply descends with the off-center wavelength, image quality is affected.Therefore, the individual layer diffraction optical element can only be used for the optical system of limited wavestrip width.In recent years, the multilayer diffraction optical element of appearance had overcome this shortcoming, had realized the raising of broadband diffraction efficiency.

At present, the diffraction efficiency of the diffraction optical element of the methods analyst folding/diffraction hybrid optical system of common employing scalar diffraction theory, the method for employing bandwidth integral mean diffraction efficiency and optical system optical transfer function product is estimated in advance and is rolled over/spread out the hybrid optical system image quality.Rolling over/spreading out in the hybrid optical system design process, adopting the design of two steps usually, the first step adopts optical design software commonly used such as zemax, codev etc. to carry out design of Optical System, and the diffraction efficiency of second step to diffraction optical element designs.In individual layer diffraction optical element design process, its design wavelength is consistent with the centre wavelength of optical system, then bandwidth integral mean diffraction efficiency is a determined value, but, in the multilayer diffraction optical element design process, the centre wavelength of multilayer diffraction optical element is the centre wavelength of optical system, has many group design wavelengths simultaneously, then the bandwidth integral mean diffraction efficiency of Dui Ying multilayer diffraction optical element is different, and the influence of the doubling/hybrid optical system that spreads out is also different.

About the optimal design of multilayer diffraction optical element, also there is not a kind of scientific and reliable method for designing at present.The design wavelength of the visible light wave range multilayer diffraction optical element of existing report is chosen as F light and C light, the perhaps two ends of wave band, carry out the high computational of the surface micro-structure of multilayer diffraction optical element by the optical material of design wavelength and selection, do not consider whether bandwidth integral mean diffraction efficiency is maximum.

Summary of the invention

The objective of the invention is to realize the maximization of multiple dielectric layer optical design bandwidth integral mean diffraction efficiency, propose a kind of Optimization Design of multilayer diffraction optical element for this reason.

Because the structure of multilayer diffraction optical element has various ways, no matter how version changes, and can equivalence become a divergence type multilayer diffraction optical element.

The present invention's method specifically comprises following step:

1, according to the surface micro-structure height formula of multilayer diffraction optical element, optimized choice constitutes the optical material of multilayer diffraction optical element;

2, in whole service band, adopt different design wavelength combinations, determine bandwidth integral mean diffraction efficiency distribution;

3, in whole service band, determine maximum bandwidth integral mean diffraction efficiency, and corresponding design wavelength;

4, that will determine and the surface micro-structure height formula corresponding design wavelength substitution of maximum bandwidth integral mean diffraction efficiency multilayer diffraction optical element calculate the surface micro-structure height of optimization of multilayer diffraction optical element and the diffraction efficiency of optimization.

Utilize the bandwidth integral mean diffraction efficiency of multilayer diffraction optical element, at 0.4～0.7 μ m visible light wave range, with polymethacrylate and polycarbonate is base material, when being design wavelength with 0.4 μ m and 0.7 μ m, the microstructure height of each layer harmonic diffraction element is respectively 17.372 μ m and 13.476 μ m, and the bandwidth integral mean diffraction efficiency that obtains is 95.319%; And with the F spectral line, when the C spectral line is design wavelength, the microstructure height of each layer harmonic diffraction element is respectively 24.171 μ m and 19.261 μ m, and resulting bandwidth integral mean diffraction efficiency is 96.832%.Its technique effect of the present invention's method is, it is 99.253% that employing the present invention's method obtains maximum bandwidth integral mean diffraction efficiency, corresponding design wavelength is 0.435 μ m and 0.598 μ m, the microstructure height of each layer harmonic diffraction element is respectively 16.460 μ m and 12.813 μ m, resulting bandwidth integral mean diffraction efficiency is than 0.4 μ m and 0.7 μ m, and 0.435 μ m and 0.598 μ m when being design wavelength, difference high 3.934% and 2.241%, and the surface micro-structure height of each layer harmonic diffraction element is all little, realized optimal design to multilayer diffraction optical element, can realize the bandwidth integral mean diffraction efficiency maximization design of multilayer diffraction optical element, solve the optimized choice problem of the design wavelength in the design.

Description of drawings

Fig. 1 is the structural representation of multilayer diffraction optical element.

The relation of diffraction efficiency and wavelength when Fig. 2 is 0.4 μ m and 0.7 μ m for the design wavelength of multilayer diffraction optical element.

The relation of diffraction efficiency and wavelength when Fig. 3 is 0.486 μ m and 0.656 μ m for the design wavelength of multilayer diffraction optical element.

Fig. 4 is second design wavelength when being the arbitrary value of 0.4 μ m～0.7 μ m, the maximum bandwidth integral mean diffraction efficiency of multilayer diffraction optical element and the variation relation of first design wavelength.

Fig. 5 is first design wavelength when being the arbitrary value of 0.4 μ m～0.7 μ m, the maximum bandwidth integral mean diffraction efficiency of multilayer diffraction optical element and the variation relation of second design wavelength.

Fig. 6 be the bandwidth product component efficiency of multilayer diffraction optical element when maximum diffraction efficiency and the relation of wavelength.

Fig. 7 is the relation of diffraction efficiency and wavelength under three kinds of different situations of the design wavelength of multilayer diffraction optical element, and this figure double as is a Figure of abstract.

Embodiment

Further specify the present invention's method below, the structure of multilayer diffraction optical element is seen shown in Figure 1, and the number of plies is double-deck.

The first step, according to the surface micro-structure height formula of multilayer diffraction optical element, optimized choice constitutes the optical material of multilayer diffraction optical element.Phase delay φ (λ) expression formula according to diffraction optical element in the scalar diffraction theory:

φ(λ)＝k[n ₁(λ)-1]H ₁+k[n ₂(λ)-1]H ₂ (1)

In the formula: λ is an operation wavelength, and k is wave number and k=2 π/λ, n ₁(λ) and n ₂(λ) be respectively the refractive index of multilayer diffraction optical element optical material when wavelength is λ, H ₁And H ₂Be respectively the surface micro-structure height of each layer of multilayer diffraction optical element.Optical material and design wavelength lambda when multilayer diffraction optical element ₁, λ ₂After determining, the phase delay of multilayer diffraction optical element is formed a linear equation in two unknowns group:

$\left\{\begin{array}{c}{k}_1((n_1\left({\mathrm{\&lambda;}}_1\right)-1){\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="HSA00000044973500011.png,HSA00000044973500022.png"\; state="\{\{state\}\}">H</figure-callout>}}_1+(n_2\left({\mathrm{\&lambda;}}_1\right)-1)H_2)=\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HSA00000044973500011.png"\; state="\{\{state\}\}">m</figure-callout>}2\mathrm{\&pi;}\\ k_2((n_1\left({\mathrm{\&lambda;}}_2\right)-1){\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="HSA00000044973500011.png,HSA00000044973500022.png"\; state="\{\{state\}\}">H</figure-callout>}}_1+(n_2\left({\mathrm{\&lambda;}}_2\right)-1)H_2)=\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HSA00000044973500011.png"\; state="\{\{state\}\}">m</figure-callout>}2\mathrm{\&pi;}\end{array}\right.---\left(2\right)$

Usually get the order of diffraction time m=1, by finding the solution linear equation in two unknowns group (2), obtaining multilayer diffraction optical element is λ at design wavelength ₁, λ ₂The time the surface micro-structure height H ₁, H ₂:

${\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="HSA00000044973500011.png,HSA00000044973500022.png"\; state="\{\{state\}\}">H</figure-callout>}}_1=\frac{{\mathrm{m\&lambda;}}_1(n_2\left({\mathrm{\&lambda;}}_2\right)-1)-{\mathrm{m\&lambda;}}_2(n_2\left({\mathrm{\&lambda;}}_1\right)-1)}{(n_1\left({\mathrm{\&lambda;}}_1\right)-1)(n_2\left({\mathrm{\&lambda;}}_2\right)-1)-(n_1\left({\mathrm{\&lambda;}}_2\right)-1)(n_2\left({\mathrm{\&lambda;}}_1\right)-1)}---\left(3\right)$

${\mathrm{<figure-callout\; id="2"\; label="H"\; filenames="HSA00000044973500011.png"\; state="\{\{state\}\}">H</figure-callout>}}_2=\frac{{\mathrm{m\&lambda;}}_2(n_1\left({\mathrm{\&lambda;}}_1\right)-1)-{\mathrm{m\&lambda;}}_1(n_1\left({\mathrm{\&lambda;}}_2\right)-1)}{(n_1\left({\mathrm{\&lambda;}}_1\right)-1)(n_2\left({\mathrm{\&lambda;}}_2\right)-1)-(n_1\left({\mathrm{\&lambda;}}_2\right)-1)(n_2\left({\mathrm{\&lambda;}}_1\right)-1)}---\left(4\right)$

After the design wavelength of multilayer diffraction optical element is determined, and one of them is high index of refraction, low dispersion optical material for the material of selecting, when another is low-refraction, high-dispersive optical material, denominator maximum, then the surface micro-structure height minimum of multilayer diffraction optical element in the surface micro-structure height formula (3) of multilayer diffraction optical element, (4).

Second step, in whole service band, adopt different design wavelength combinations, determine bandwidth integral mean diffraction efficiency distribution.After the optical material of multilayer diffraction optical element and design wavelength were determined, then the surface micro-structure height of multilayer diffraction optical element also was a determined value, the diffraction efficiency that the m order of diffraction of multilayer diffraction optical element is inferior _m(λ) be:

${\mathrm{\&eta;}}_m\left(\mathrm{\&lambda;}\right)={\sin c}^2(m-\frac{\mathrm{\&phi;}\left(\mathrm{\&lambda;}\right)}{2\mathrm{\&pi;}})---\left(5\right)$

Wherein, $\sin c\left(x\right)=\frac{\sin \left(\mathrm{\&pi;x}\right)}{\mathrm{\&pi;x}}$

At the multilayer diffraction optical element design wavelength is λ ₁, λ ₂The time, the bandwidth integral mean diffraction efficiency that the m order of diffraction is inferior _Mint(λ ₁, λ ₂) be:

${\stackrel{\&OverBar;}{\mathrm{\&eta;}}}_{\min t}({\mathrm{\&lambda;}}_1,{\mathrm{\&lambda;}}_2)=\frac{1}{{\mathrm{\&lambda;}}_{\max }-{\mathrm{\&lambda;}}_{\min }}\underset{{\mathrm{\&lambda;}}_{\min }}{\overset{{\mathrm{\&lambda;}}_{\max }}{\&Integral;}}{\mathrm{\&eta;}}_m\left(\mathrm{\&lambda;}\right)\mathrm{d\&lambda;}---\left(6\right)$

In the formula: λ _Min, λ _MaxMinimum wavelength and the maximum wavelength of representing service band respectively.

The 3rd step, in whole service band, determine maximum bandwidth integral mean diffraction efficiency, and corresponding design wavelength.After the material that constitutes multilayer diffraction optical element is determined, work as design wavelength lambda ₁, λ ₂When being a pair of different variable quantity, according to formula (6) as can be known the bandwidth integral mean diffraction efficiency of multilayer diffraction optical element also changing.Work as design wavelength lambda ₁Be a fixed wave length, λ ₂Be one from minimum wavelength λ _MinTo maximum wavelength λ _MaxBetween any value the time, have the bandwidth integral mean diffraction efficiency of a maximum _Mint(λ ₁) _Max, then can draw out the different designs wavelength X according to this principle ₁The time the variation diagram of maximum bandwidth integration diffraction.In like manner, work as design wavelength lambda ₂Be a fixed wave length, λ ₁Be one from minimum wavelength λ _MinTo maximum wavelength λ _MaxBetween any value the time, have the bandwidth integral mean diffraction efficiency of a maximum _Mint(λ ₂) _Max, then draw out the different designs wavelength X according to this principle ₂The time the variation diagram of maximum bandwidth integration diffraction.Definition, maximum bandwidth integral mean diffraction efficiency and first design wavelength lambda according to bandwidth integral mean diffraction efficiency ₁Maximum bandwidth integral mean diffraction efficiency distribution figure, and maximum bandwidth integral mean diffraction efficiency and second design wavelength lambda ₂Maximum bandwidth integral mean diffraction efficiency distribution figure, the design wavelength of the maximum bandwidth integral mean diffraction efficiency correspondence of multilayer diffraction optical element is a pair of symmetric points as can be known, the bandwidth integral mean diffraction efficiency of multilayer diffraction optical element can reach maximization, i.e. (λ ₁, λ ₂, η _Mmax) and (λ ₂, λ ₁, η _Mmax), then Dui Ying design wavelength is the design wavelength of the maximized multilayer diffraction optical element of bandwidth integral mean diffraction efficiency.

The 4th step, with that determine and the surface micro-structure height formula corresponding design wavelength substitution of maximum bandwidth integral mean diffraction efficiency multilayer diffraction optical element, calculate the surface micro-structure height of optimization of multilayer diffraction optical element and the diffraction efficiency of optimization.Determine design wavelength according to maximum bandwidth integral mean diffraction efficiency, design wavelength is brought into surface micro-structure height formula (3), (4) of multilayer diffraction optical element, obtain the surface micro-structure height of multilayer diffraction optical element, the surface micro-structure height of optimized multilayer diffraction optical element is brought into the phase delay expression formula (1) of diffraction optical element, according to the inferior diffraction efficiency formula (5) of the m order of diffraction of multilayer diffraction optical element, obtain the inferior diffraction efficiency of the m order of diffraction of optimized multilayer diffraction optical element again.

Multilayer diffraction optical element with high index of refraction, low dispersion optical material N-FK51A and the low-refraction that adopts German Schott AG, high chromatic dispersion material P-SF67 is the method that example further specifies the present invention below.

When the design wavelength of multilayer diffraction optical element is selected wave band two ends 0.4 μ m and 0.7 μ m, the surface micro-structure height of multilayer diffraction optical element is respectively 8.674 μ m and 3.934 μ m, bandwidth integral mean diffraction efficiency is 95.524%, and diffraction efficiency distribution is seen shown in Figure 2.When the design wavelength of multilayer diffraction optical element is selected F (0.4861 μ m) spectral line and C (0.6563 μ m) spectral line, the surface micro-structure height of multilayer diffraction optical element is respectively 11.700 μ m and 5.606 μ m, bandwidth integral mean diffraction efficiency is 97.032%, and diffraction efficiency distribution is seen shown in Figure 3.

When designing multilayer diffraction optical element according to above-mentioned employing bandwidth integral mean diffraction efficiency maximization, the bandwidth integral mean diffraction efficiency of multilayer diffraction optical element and the relation between first design wavelength are seen shown in Figure 4, see shown in Figure 5 with the relation of second design wavelength.According to Fig. 4 and Fig. 5, the design wavelength of the maximum bandwidth integral mean diffraction efficiency correspondence of multilayer diffraction optical element is a pair of symmetric points as can be known, has realized the maximization of the bandwidth integral mean diffraction efficiency of multilayer diffraction optical element, and promptly working as design wavelength is λ ₁=0.435 μ m, λ ₂=0.598 μ m, η _Mmax=99.288%, work as λ ₁=0.598 μ m, λ ₂=0.435 μ m, η _Mmax=99.288%, then Dui Ying design wavelength is the design wavelength of the maximized multilayer diffraction optical element of bandwidth integral mean diffraction efficiency.

When the design wavelength of multilayer diffraction optical element is 0.435 μ m and 0.598 μ m, the surface micro-structure height of multilayer diffraction optical element is respectively 8.186 μ m and 3.739 μ m, bandwidth integral mean diffraction efficiency is 99.288%, and diffraction efficiency distribution is seen shown in Figure 6.

According to formula (5), obtain the diffraction efficiency of distinct methods

Diffraction efficiency during the design wavelength determined with process according to the invention

Distribute, see shown in Figure 7.

Claims (3)

1. the Optimization Design of a multilayer diffraction optical element is characterized in that, (1) according to the surface micro-structure height formula of multilayer diffraction optical element, optimized choice constitutes the optical material of multilayer diffraction optical element; (2) in whole service band, adopt different design wavelength combinations, determine bandwidth integral mean diffraction efficiency distribution; (3) in whole service band, determine maximum bandwidth integral mean diffraction efficiency, and corresponding design wavelength; (4) that will determine and the surface micro-structure height formula corresponding design wavelength substitution of maximum bandwidth integral mean diffraction efficiency multilayer diffraction optical element calculate the surface micro-structure height of optimization of multilayer diffraction optical element and the diffraction efficiency of optimization.

2. the Optimization Design of multilayer diffraction optical element according to claim 1 is characterized in that, the surface micro-structure height formula of described multilayer diffraction optical element is:

$H_1=\frac{m{\mathrm{\&lambda;}}_1(n_2\left({\mathrm{\&lambda;}}_2\right)-1)-m{\mathrm{\&lambda;}}_2(n_2\left({\mathrm{\&lambda;}}_1\right)-1)}{(n_1\left({\mathrm{\&lambda;}}_1\right)-1)(n_2\left({\mathrm{\&lambda;}}_2\right)-1)-(n_1\left({\mathrm{\&lambda;}}_2\right)-1)(n_2\left({\mathrm{\&lambda;}}_1\right)-1)},$

$H_2=\frac{m{\mathrm{\&lambda;}}_2(n_1\left({\mathrm{\&lambda;}}_1\right)-1)-m{\mathrm{\&lambda;}}_1(n_1\left({\mathrm{\&lambda;}}_2\right)-1)}{(n_1\left({\mathrm{\&lambda;}}_1\right)-1)(n_2\left({\mathrm{\&lambda;}}_2\right)-1)-(n_1\left({\mathrm{\&lambda;}}_2\right)-1)(n_2\left({\mathrm{\&lambda;}}_1\right)-1)},$

In the formula: H ₁And H ₂Be respectively the surface micro-structure height of each layer of multilayer diffraction optical element, m is that the order of diffraction is inferior, λ ₁, λ ₂Be the design wavelength of multilayer diffraction optical element, n ₁(λ ₁), n ₁(λ ₂), n ₂(λ ₁) and n ₂(λ ₂) be respectively the refractive index of multilayer diffraction optical element optical material to design wavelength.

3. the Optimization Design of multilayer diffraction optical element according to claim 1 is characterized in that, described bandwidth integral mean diffraction efficiency is tried to achieve by following formula:

${\stackrel{\&OverBar;}{\mathrm{\&eta;}}}_{\mathrm{m\; int}}({\mathrm{\&lambda;}}_1,{\mathrm{\&lambda;}}_2)=\frac{1}{{\mathrm{\&lambda;}}_{\max }-{\mathrm{\&lambda;}}_{\min }}\underset{{\mathrm{\&lambda;}}_{\min }}{\overset{{\mathrm{\&lambda;}}_{\max }}{\&Integral;}}{\mathrm{\&eta;}}_m\left(\mathrm{\&lambda;}\right)\mathrm{d\&lambda;},$

In the formula: η _{M int}(λ 1, and λ 2) is the inferior bandwidth integral mean diffraction efficiency of the m order of diffraction, λ _Min, λ _MaxMinimum wavelength and the maximum wavelength of representing service band respectively, η _m(λ) be the inferior diffraction efficiency of the m order of diffraction.

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