Review of Design Methods of Diffractive Optical Element

$Design examples of Diffraction Tools @ BIT［21-22］. (a) Intensity distribution of original image; (b) intensity distribution of reconstructed image; (c) reconstruction error varying with number of iterations; (d) optical setup of image decryption system with polarization DOE; (e) designed surface relief pattern of polarized DOE; (f) decryption image$

Fig. 4. Design examples of Diffraction Tools @ BIT^［21-22］. (a) Intensity distribution of original image; (b) intensity distribution of reconstructed image; (c) reconstruction error varying with number of iterations; (d) optical setup of image decryption system with polarization DOE; (e) designed surface relief pattern of polarized DOE; (f) decryption image

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Fig. 5. Schematic diagram of two DOEs and two output layers^[67]

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$Diffraction deep neural network based on DOE[69]. (a) DOEs manufactured by 3D printing; (b) schematic diagram of cascaded DOEs for handwritten digit classification$

Fig. 6. Diffraction deep neural network based on DOE^[69]. (a) DOEs manufactured by 3D printing; (b) schematic diagram of cascaded DOEs for handwritten digit classification

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Fig. 7. Algorithm flow chart for designing DOE that can generate beam with ultrahigh aspect ratio^[89]

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Fig. 8. DOE that can realize controllable spin beam^[101]. (a) DOE phase distribution;(b) spin light field distribution at different exit distances

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Fig. 9. DOE for spectral separation^[103]

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Fig. 10. Polarization filter array and focal plane array sensor^[124]

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Fig. 11. Reasons for astigmatism in HOE^[141]

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$Two methods for processing and optimizing DOE[142]. (a) Using refractive freeform surface element; (b) using holographic printing system$

Fig. 12. Two methods for processing and optimizing DOE^[142]. (a) Using refractive freeform surface element; (b) using holographic printing system

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Table 1. Comparison of common design algorithms

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Table 1. Comparison of common design algorithms

Algorithm	Type	Characteristic of solution	Advantage	Limitation
GS algorithm	Iteration	Local optimum	High calculation speed，simple structure	Sensitive to initial conditions，only applicable to unitary optical transformation system
YG algorithm	Iteration	Local optimum	High calculation speed，suitable for any optical transformation system	Sensitive to initial conditions
Hill-Climbing algorithm	Search	Local optimum	Simple structure	Sensitive to initial conditions，low calculation speed
SA algorithm	Search	Global optimum	Simple structure，strong robustness	Slow convergence，sensitive to parameter
Genetic algorithm	Search	Global optimum	Parallel operation	Slow evolution，premature convergence
Deep learning	Learning	Global optimum	Accurate results，high calculation speed	Long training time，sensitive to training data

Table 2. Common auxiliary tools for designing DOE

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Table 2. Common auxiliary tools for designing DOE

Software

Developer

Principle

Major function

Characteristic

Virtuallab Fusion

Jena University，Germany

Diffraction and interference of light

Component and system design for imaging，detection and shaping

Solver integrating geometry and wave optics

DOE Master

Light Soft，America

Diffraction and interference of light

Design of DOE

Multiple optimization algorithms，design cascade DOE

Diffraction Tools @

BIT

Beijing Institute of Technology，China

Diffraction，interference and polarization of light

Design of micro-optics and DOE

Multiple design modules，

joint optimization of complex optical systems

Table 3. Comparison of DOE processing methods

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Table 3. Comparison of DOE processing methods

Fabrication method	Mask	Projection system	Point-by-point method	Source of error
Binary mask lithography［26］	√	×	×	Mask alignment，line width，depth
Grayscale mask lithography［27-28］	√	×	×	Nonlinear error
Thin film deposition technology［29］	√	×	×	Mask alignment，coating thickness
Particle beam projection lithography［30］	√	√	×	Mask displacement，mask deformation，particle scattering
Sub-wavelength holographic lithography［31-35］	√	×	×	Holographic mask calculation，mask alignment
Diamond turning［36］	×	×	√	Residual knife mark，surface profile
Particle beam direct writing lithography［37-38］	×	×	√	Proximity effect，substrate location，processing environment
Imprint［39-40］	×	×	×	Mold，viscous deformation，elastic deformation
Injection molding［41］	×	×	×	Mold，viscous deformation，elastic deformation
Digital lithography［42-46］	×	×	×	Discrete of DMD pixel elements，illumination uniformity
Femtosecond laser direct writing［47-49］	×	×	√	Mechanical displacement，proximity effect
Laser interference lithography［50-53］	×	×	×	Material nonlinearity，loss of high frequency

Table 4. Parameters of typical dynamic DOE

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Table 4. Parameters of typical dynamic DOE

Material	Function	Tuning mode	Mask	Response time	Driving voltage
Liquid crystal［159］	Switchable	Electrical	×	15 ms/50 ms	20 V
Azo-benzene functionalized polymer film［161］	Rewritable	Electrical/optical/thermal	×	Dozens of minutes	8 kV@130 ℃
Liquid crystal［162］	Switchable	Electrical	×		6 V
Hybrid nematic liquid crystal［164］	Switchable/ rewritable	Electrical/optical	√	1 ms
Blue phase liquid crystal［163］	Switchable	Electrical	×	545 μs/673 μs	180 V
Chiral liquid crystals［166］	Rewritable	Electrical/optical	×	100 μs	~175 V
Blue phase liquid crystal［165］	Rewritable	Electrical/optical	√	16 min	10 V
Liquid crystal［167］	Tunable	Optical	√	24 min
Holographic polymer-dispersed Liquid crystals［169］	Rewritable	Optical	×	40 s
Cholesteric liquid crystal［168］	Rewritable	Optical	√	17 min/90 s	10 V（erase）