An optimization algorithm for a multi-focal diffractive lens

Abstract

The application provides an optimization algorithm of a multi-focus diffractive lens, which comprises the following steps: determining the number of focal points, the diffraction order of each focal point and the target diffraction efficiency of each focal point according to actual application requirements; randomly assigning an initial phase to each focal point and calculating the complex amplitude of light waves; cyclically modulating the complex amplitude of light waves and the diffraction efficiency of each focal point by using a phase retrieval method; and determining the change relationship between the complex amplitude of light waves after modulation and the radial distance of the wave front from the distance pupil center by using the modulation method. By the method of the application, a multi-focus diffractive lens with no sharp corner, higher diffraction efficiency and freely controllable diffraction efficiency of each focal point can be designed.

Description

Technical Field

[0001] This invention belongs to the field of optometry and relates to a design method for multifocal diffractometers, specifically an optimization algorithm for multifocal diffractometers. Background Technology

[0002] Presbyopia is a symptom that everyone develops as they age. It manifests as a loss of the eye's ability to focus, allowing the eye to see objects clearly only at a certain distance. There are various methods to correct presbyopia, such as corrective glasses, multifocal corrective glasses, contact lenses, and artificial lenses.

[0003] Existing multifocal lenses can be divided into multifocal diffractive lenses and multifocal refractive lenses based on their optical properties. The working principle of a multifocal refractive lens is to create different refractive regions on the lens surface, each with its own refractive power. The working principle of a multifocal diffractive lens is to create a grating structure on the lens surface, thereby utilizing the diffraction effect to achieve multiple focal points. Figure 1 This is a typical side cross-sectional diagram of a multifocal diffractometer. Its grating structure has many sharp corners, which leads to several problems. First, it increases the manufacturing difficulty of multifocal diffractometers because sharp corners are difficult to manufacture precisely; they are often rounded during manufacturing, affecting diffraction. Second, the jump height of each grating structure (i.e., the vertical depth of the sharp corner segment) is also difficult to control precisely. Errors will cause changes in the optical performance of the multifocal diffractometer. These disadvantages apply to intraocular lenses. For contact lenses, on the one hand, the tear film interferes with the optical performance of this grating structure with multiple sharp corners; on the other hand, this grating structure can rub against the eyelids, causing discomfort to the wearer. Furthermore, the energy utilization rate (i.e., diffraction efficiency) of this grating structure is low, generally not exceeding 85%. Therefore, this grating structure with multiple sharp corners cannot be used in contact lenses.

[0004] A sinusoidal grating can solve the above problems. Figure 2 This is a typical side profile of a sinusoidal grating. Sinusoidal gratings have no sharp edges and offer relatively higher energy efficiency, reaching over 90%. However, unlike gratings with multiple sharp corners, sinusoidal gratings cannot freely control the energy at each focal point. Therefore, improving existing multifocal diffraction mirror design methods to create multifocal diffraction mirrors without sharp edges, with higher diffraction efficiency, and where the diffraction efficiency at each focal point can be arbitrarily adjusted would be highly beneficial in solving the aforementioned problems. Summary of the Invention

[0005] To address the issues of sharp corners and low diffraction efficiency in the grating structures of multifocal diffractometers designed using existing methods, or the inability to freely control the diffraction efficiency of each focus despite the absence of sharp corners and relatively high diffraction efficiency, this invention provides an optimization algorithm for multifocal diffractometers. This algorithm utilizes phase retrieval to design multifocal diffractometers with sharp corner-free grating structures, higher diffraction efficiency, and freely adjustable diffraction efficiency at each focus.

[0006] To achieve the above-mentioned objectives, the technical solution adopted by the present invention is as follows:

[0007] An optimization algorithm for a multifocal diffractometer includes the following steps:

[0008] ① Determine the number of focal points, the diffraction order of each focal point, and the target diffraction efficiency of each focal point based on actual application requirements. Let the number of focal points be denoted as n, where n is an integer and n≥2. Let the diffraction order of each focal point be denoted as l, where l=l1,l2,…,ln, and l1,l2,…,ln are distinct integers. Let the target diffraction efficiency of the focal point with diffraction order l be denoted as |a ltarget | 2 ;

[0009] ② Randomly assign an initial phase arg(a) to each focus. l ), calculate the component a of each focal point according to equation (1) l Then, the complex amplitude CA of the light wave is calculated using equation (3).

[0010] a l =arg(a l )*|a l target | (1)

[0011]

[0012]

[0013] In equations (1) to (3), a l It is a complex number, arg is the argument function, arg(a) l ) represents the phase of the focus with diffraction order l, |a ltarget | represents the target amplitude at the focal point with diffraction order l, || represents the absolute value sign, arg represents the argument function, exp represents the exponent sign, i represents the imaginary number sign, and W represents the absolute value sign. m The basic wavefront is defined as follows: r is the radial distance from the center of the pupil, R is the design radius, λ is the wavelength of the light wave, and l is the diffraction order at the focal point.

[0014] ③ The phase restoration method is used to cyclically modulate the complex amplitude CA of the light wave and the component a at the focal point with diffraction order l. l and diffraction efficiency |a l | 2 ,

[0015] That is, according to equation (4), |CA| is modulated into |CA′|, arg(CA) and |CA′| are combined into CA′ according to equation (5), and then a is calculated according to equation (6). l ′, from equation (7) |a l ′| 2 Modulated to |a l | 2 Calculate the component a of each focal point according to equation (8). l Then, the a calculated from equation (8) l Substitute into equation (3) to calculate the complex amplitude CA of the light wave.

[0016] |CA′|=f1(|CA|) (4)

[0017] CA′=exp(iarg(CA))*|CA′| (5)

[0018]

[0019] |a l | 2 =f2(|a l ′| 2 (7)

[0020] a l =exp(iarg(a l ′))*|a l | (8)

[0021] In equations (4) to (8), CA is the complex amplitude of the light wave, CA′ is the modulated complex amplitude of the light wave, and a l ′ is the modulated a l ,|a l | 2 Let |a| be the diffraction efficiency of the focal point with diffraction order l. l ′| 2 Let be the diffraction efficiency at the focal point with modulated diffraction order l, || denotes the absolute value sign, arg denotes the argument function, and arg(a) l ′) represents the phase of the focal point of the modulated diffraction order l; ρ = r 2 r is the radial distance from the center of the pupil; R is the design radius; λ is the wavelength of light; exp is the exponent symbol; i is the imaginary number symbol; W m The fundamental wavefront is l, which is the diffraction order at the focal point; f1 and f2 are the modulation functions.

[0022] Repeat the above steps until... Approaching 1 and |a l |approaching|a ltarget |;

[0023] ④ From step ③ Approaching 1 and |a l |approaching|a ltarget The complex amplitude CA of the light wave corresponding to the time is determined according to equation (9) to determine the relationship between the wavefront and the radial distance from the center of the pupil.

[0024]

[0025] In equation (9), W is the light wavefront of the final multifocal diffractometer, and CA is... Approaching 1 and |a l |approaching|a ltarget | The corresponding complex amplitude CA of the light wave, where arg is the amplitude angle function and λ is the wavelength of the light wave.

[0026] In the above-mentioned optimization algorithm for multifocal diffractometers, the phase restoration method in step ③ includes, but is not limited to, at least one of the error attenuation method and the hybrid input-output method. For example, the error attenuation method and the hybrid input-output method can be used separately, or the error attenuation method and the hybrid input-output method can be used alternately.

[0027] In the above-mentioned optimization algorithm for multifocal diffractometers, the expression for modulation function f1 in the error attenuation method can be shown in equation (10), and the expression for modulation function f2 can be shown in equation (11).

[0028] |CA′|=t1|CA|+(1-t1) (10)

[0029] |a l | 2 =t2|a l ′| 2 +(1-t2)|a l target | 2 (11)

[0030] In equations (10) to (11), t1 and t2 are modulation variables, t1 is 0 to 1, t2 is 0 to 1, CA is the complex amplitude of the light wave, CA′ is the complex amplitude of the modulated light wave, || is the sign of taking the absolute value, and |a ltarget | 2 For the target diffraction efficiency at the focal point with diffraction order l, |a l | 2 Let |a| be the diffraction efficiency of the focal point with diffraction order l. l ′|2 Let be the diffraction efficiency of the focal point with modulated diffraction order l.

[0031] In the above-mentioned optimization algorithm for multifocal diffractometers, the operation of the hybrid input-output method is as follows:

[0032] Repeat step ③ q times, and the component a at the focal point with diffraction order l is obtained. l denoted as a lq The diffraction efficiency of a focal point with a diffraction order of l is denoted as |a''. lq ′| 2 If ||a lq ′| 2 -|a ltarget | 2 If |<E0, where E0 is the target deviation, then the component a of the focus with diffraction order l obtained in the q-th cycle is... l Reverse compensation is performed according to formula (11).

[0033] Soon a lq Adjusted according to equation (12) Then the result obtained from equation (12) As a l Substitute into equation (3) to calculate the complex amplitude CA of the light wave.

[0034]

[0035] In equation (12), q is the number of iterations, 0 < β ≤ 1. Let a be the amplitude of the focus of the diffraction order l obtained in the (q-1)th cycle. lq ′ is the component a of the focus with diffraction order l obtained in the qth cycle. l , It is the amplitude of the focus with diffraction order l obtained in the qth cycle;

[0036] If ||a lq ′| 2 -|a ltarget | 2 If |≥E0, and E0 is the target deviation, then it is not necessary to apply equation (11) to the component a of the focal point with diffraction order l. l Perform reverse compensation;

[0037] Repeat the above steps until... Approaching 1 and |a l |approaching|a ltarget |

[0038] More specifically, the operation of the hybrid input / output method is as follows:

[0039] S1, modulate |CA| into |CA′| according to equation (4), combine arg(CA) and |CA′| into CA′ according to equation (5), and then calculate a according to equation (6). l ′, from equation (7) |a l ′| 2 Modulated to |a l | 2 Calculate the component a of each focal point according to equation (8). l Then, the a calculated from equation (8) l Substitute into equation (3) to calculate the complex amplitude CA of the light wave.

[0040] |CA′|=f1(|CA|) (4)

[0041] CA′=exp(iarg(CA))*|CA′| (5)

[0042]

[0043] |a l | 2 =f2(|a l ′| 2 (7)

[0044] a l =exp(iarg(a l ′))*|a l | (8)

[0045] In equations (4) to (8), CA is the complex amplitude of the light wave, CA′ is the modulated complex amplitude of the light wave, and a l ′ is the modulated a l ,|a l | 2 Let |a| be the diffraction efficiency of the focal point with diffraction order l. l ′| 2 Let |a| be the diffraction efficiency of the focal point with modulated diffraction order l. ltarget | 2 Let be the diffraction efficiency of the target at the focal point with diffraction order l, || denotes the absolute value sign, arg is the argument function, and arg(a) l ) represents the phase of the focus at diffraction order l, arg(a) l ′) represents the phase of the focal point of the modulated diffraction order l; ρ = r 2 r is the radial distance from the center of the pupil; R is the design radius; λ is the wavelength of light; exp is the exponent symbol; i is the imaginary number symbol; W m With the fundamental wavefront, l is the diffraction order at the focal point; f1 and f2 are the modulation functions; repeat the above steps continuously until... Approaching 1 and |al |approaching|a ltarget |;

[0046] S2, repeat the operation of step S1, and after q cycles, the component a of the focal point with diffraction order l is obtained. l denoted as a lq The diffraction efficiency of a focal point with diffraction order l is denoted as |q''. lq ′| 2 If ||q lq ′| 2 -|a ltarget | 2 If |<E0, where E0 is the target deviation, then the component a of the focus with diffraction order l obtained in the q-th cycle is... l Reverse compensation is performed according to formula (11).

[0047] Soon Q lq Adjusted according to equation (12) Then the result obtained from equation (12) As a l Substitute into equation (3) to calculate the complex amplitude CA of the light wave.

[0048]

[0049] In equation (12), q is the number of iterations, 0 < β ≤ 1. Let a be the amplitude of the focus of the diffraction order l obtained in the (q-1)th cycle. lq ′ is the component a of the focus with diffraction order l obtained in the qth cycle. l , It is the amplitude of the focus with diffraction order l obtained in the qth cycle;

[0050] If ||a lq ′| 2 -|a ltarget | 2 If |≥E0, and E0 is the target deviation, then it is not necessary to apply equation (11) to the component a of the focal point with diffraction order l. l Perform reverse compensation and continue the loop of step S1;

[0051] Repeat steps S1 and S2 until... Approaching 1 and |a l |approaching|a ltarget |

[0052] Furthermore, in the above-mentioned optimization algorithm for multifocal diffractometers, when the hybrid input-output method is adopted, the value of the target deviation E0 is determined according to the actual application requirements. For example, the target deviation E0 can usually be between 0 and 0.05.

[0053] Furthermore, in the above-mentioned optimization algorithm for the multifocal diffractometer, in the hybrid input-output method, the expression for the modulation function f1 can be as shown in equation (10), and the expression for the modulation function f2 can be as shown in equation (11).

[0054] |CA′|=t1|CA|+(1-t1) (10)

[0055] |a l | 2 =t2|a l ′| 2 +(1-t2)|a ltarget | 2 (11)

[0056] In equations (10) to (11), t1 and t2 are modulation variables, with t1 being 0 to 1 and t2 being 0 to 1.

[0057] In the above-mentioned optimization algorithm for multifocal diffractometers, the... Approaching 1 means It is between 0.75 and 1.

[0058] In the above-mentioned optimization algorithm for multifocal diffractometers, the design radius R is equal to or not equal to the pupil radius of the person using the multifocal diffractometer. Further, the design radius R is 1.0 to 1.5 times the pupil radius of the person using the multifocal diffractometer.

[0059] In the above-mentioned optimization algorithm for multifocal diffractometers, the wavelength λ is determined according to the actual application requirements. For example, the wavelength λ can be within the visible light wavelength range or outside the visible light wavelength range.

[0060] In the above-mentioned optimization algorithm for multifocal diffractometers, as the number of focal points gradually increases, the imaging quality of the diffractometer designed by this optimization method gradually exhibits the characteristics of continuous depth of field.

[0061] In the above-mentioned optimization algorithm for multifocal diffractometers, the final obtained relationship between the wavefront W of the multifocal diffractometer and the radial distance from the pupil center can be rotationally symmetrical about the pupil center, such as... Figure 4 As shown.

[0062] The optimization algorithm for multifocal diffractors provided by this invention is applicable to the design of multifocal diffractors used by the human eye, as well as the design of multifocal diffractors in optical systems.

[0063] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0064] The optimization algorithm for multifocal diffractometers provided by this invention optimizes existing multifocal diffractometer design methods by iteratively modulating the complex amplitude of the light wave and the amplitude of the focal point with diffraction order l through phase restoration. This method can design multifocal diffractometers with grating structures without sharp corners and extremely high diffraction efficiency, effectively reducing the manufacturing difficulty of diffractometers. Furthermore, this method allows for free control of the diffraction efficiency of each focal point. Compared with existing methods for designing multifocal diffractometers with multiple sharp corner structures, this invention solves the problem of high manufacturing difficulty caused by sharp corners in the grating structure of the diffractometer, and also addresses the problem of low diffraction efficiency. Compared with existing methods for designing multifocal diffractometers with sinusoidal gratings, this invention can further improve diffraction efficiency and also allows for free control of the diffraction efficiency of each focal point. Examples of this invention demonstrate that the optimized diffraction efficiency achieved using this invention has a high degree of consistency with the target diffraction efficiency, with a total diffraction efficiency exceeding 95%. Simultaneously, as the number of focal points increases, the designed diffractometer gradually exhibits refractive characteristics, achieving a continuous depth-of-field effect. Furthermore, the wavefront obtained by the optimization method of the present invention can have periodic characteristics, which can weaken the influence of pupil size and the influence of lens lateral displacement. Attached Figure Description

[0065] Figure 1 This is a typical side cross-sectional diagram of a multifocal lens with multiple sharp angles.

[0066] Figure 2 It is a typical side profile of a sinusoidal grating.

[0067] Figure 3 It shows the relationship between the wavefront height of a trifocal sawtooth diffractometer and the radial distance from the center of the pupil, as well as a schematic diagram of the complex amplitude generated by the diffractometer being decomposed into multiple sub-wavefront complex amplitudes.

[0068] Figure 4 This is a schematic diagram showing the relationship between the wavefront and the radial distance from the pupil center obtained by the optimization method of this invention, which is rotationally symmetrical around the pupil center.

[0069] Figure 5 This is the relationship between the wavefront of the light wave and the radial distance from the center of the pupil, obtained in Example 1.

[0070] Figure 6 This is a comparison chart of the target diffraction efficiency at each focal point in Example 1 and the optimized diffraction efficiency.

[0071] Figure 7 This refers to the imaging quality of the optimized multifocal diffractometer in Example 1 for object distances from -1.5D to 1.5D.

[0072] Figure 8 This is the relationship between the wavefront of the light wave and the radial distance from the center of the pupil, obtained in Example 2.

[0073] Figure 9 This is a comparison chart of the target diffraction efficiency at each focal point in Example 2 and the optimized diffraction efficiency.

[0074] Figure 10 This refers to the imaging quality of the optimized multifocal diffractometer in Example 2 for object distances from -1.5D to 1.5D.

[0075] Figure 11 This is the relationship between the wavefront of the light wave and the radial distance from the center of the pupil, obtained in Example 3.

[0076] Figure 12 This is a comparison chart of the target diffraction efficiency at each focal point in Example 3 and the optimized diffraction efficiency.

[0077] Figure 13 This refers to the imaging quality of the optimized multifocal diffractometer in Example 3 for object distances from -1.5D to 1.5D.

[0078] Figure 14 This is the relationship between the wavefront of the light wave and the radial distance from the center of the pupil, obtained in Example 4.

[0079] Figure 15 This is a comparison chart of the target diffraction efficiency at each focal point in Example 4 and the optimized diffraction efficiency.

[0080] Figure 16 This refers to the imaging quality of the optimized multifocal diffractometer in Example 4 for object distances from -1.5D to 1.5D. Detailed Implementation

[0081] The following examples further illustrate the optimization algorithm for a multifocal diffractometer provided by this invention. It should be noted that the following examples are only for further illustration of this invention and should not be construed as limiting the scope of protection of this invention. Any non-essential improvements and adjustments made by those skilled in the art based on the above description of the invention to implement it are still within the scope of protection of this invention.

[0082] Basic Definition

[0083] like Figure 3 As shown in the figure, the horizontal axis r represents the radial distance from the center of the pupil, and the vertical axis W represents the wavefront. Figure 3 The curve shows the relationship between wavefront height and radial distance from the center of the pupil. Figure 3In the diagram, the top row of 'W's represents a typical trifocal sawtooth diffractometer, which we will use as an example. The complex amplitude produced by this trifocal sawtooth diffractometer can be decomposed into a superposition of the complex amplitudes of many wavefronts. These wavefronts are as follows: Figure 3 As shown, located Figure 3 Below the W in the top row (0·W) m ,1·W m ,2·W m ,3·W m ,n·W m They all share a common characteristic: they are all based on a fundamental wavefront W. m l times, where l is an integer from negative infinity to positive infinity. Basic wavefront W m The shape, such as Figure 3 As shown in the row where l=1, the refractive power of the basic wavefront is φ. m Each fundamental wavefront corresponds to a diffraction order and also to a focal point.

[0084] For a pupil with radius R, the basic wavefront W m The definition is shown in equation (2), and its refractive power is shown in equation (13).

[0085]

[0086]

[0087] In equations (2) and (13), r is the radial distance from the center of the pupil, R is the design radius, λ is the wavelength of light, and W m Basic wavefront, φ m The refractive power of the base wavefront.

[0088] Equation (14) shows the light wavefront W and the fundamental wavefront W m The relationship between them

[0089]

[0090] In equation (15), W is the wavefront of the light wave, W m In the basic wavefront, exp is the exponent symbol, i is the imaginary symbol, λ is the wavelength of light, and a l Let a be a complex number. l The calculation formula is shown in equation (15), and at the same time a l It also satisfies equation (16),

[0091]

[0092]

[0093] In equations (15) to (16), ρ = r 2 r is the radial distance from the center of the pupil, R is the design radius, λ is the wavelength of the light wave, exp is the exponent symbol, i is the imaginary number symbol, W is the wavefront of the light wave, W m Given the fundamental wavefront, with l as the focal point, the diffraction order is |a l | 2 Let l be the diffraction efficiency of the focal point with diffraction order l.

[0094] Example 1

[0095] In this embodiment, the pupil radius of the person using the multifocal diffractometer is 3mm. Based on this pupil radius, the design radius R = 3mm is determined. According to the actual application requirements, the light wavelength λ = 550nm is determined. Taking this case as an example, the optimization algorithm of the multifocal diffractometer of the present invention is explained in detail, and the steps are as follows:

[0096] ① Based on practical application requirements, the number of focal points is determined to be 3, i.e., n=3. The diffraction order of each focal point is determined according to practical application requirements and denoted as l, l=l1,l2,…,ln. Specifically, l1=-8, l2=0, ln=l3=8. Simultaneously, the target diffraction efficiency |a| of the focal point with diffraction order l is determined according to practical application requirements. ltarget | 2 , specifically, |a -8 | 2 =0.43,|a0| 2 =0.24,|a8| 2 =0.28.

[0097] The refractive power φ of the fundamental wavefront can be calculated using equation (13). m =0.1225D (D is an abbreviation for diopters), based on the diffraction order at the three foci, from equation lφ m The refractive powers of the three focal points were calculated to be -0.98D, 0D, and 0.98D, respectively.

[0098]

[0099] In equation (13), R is the design radius, λ is the wavelength of light, and φ is the wavelength of light. m The refractive power of the base wavefront.

[0100] ② Randomly assign an initial phase arg(a) to each focus. l ), calculate the component a of each focal point according to equation (1) l Then, the complex amplitude CA of the light wave is calculated using equation (3).

[0101] a l =arg(a l)*|a ltarget | (1)

[0102]

[0103]

[0104] In equations (1) to (3), a l It is a complex number, arg is the argument function, arg(a) l ) represents the phase of the focus with diffraction order l, |a ltarget | represents the target amplitude at the focal point with a diffraction order of l. |a ltarget | 2 Let W be the target diffraction efficiency at the focal point with diffraction order l, || denotes the absolute value sign, arg denotes the argument function, exp denotes the exponent sign, i denotes the imaginary number sign, and W is the derivation of the target diffraction efficiency at the focal point with diffraction order l. m The basic wavefront is defined as r, which is the radial distance from the center of the pupil, R is the design radius, and λ is the wavelength of the light wave.

[0105] ③ The phase restoration method is used to cyclically modulate the complex amplitude CA of the light wave and the component a at the focal point with diffraction order l. l and diffraction efficiency |a l | 2 The phase restoration method used in this embodiment is the error attenuation method, and the operation is as follows:

[0106] Modulate |CA| into |CA′| according to equation (4), combine arg(CA) and |CA′| into CA′ according to equation (5), and then calculate a according to equation (6). l ′, from equation (7) |a l ′| 2 Modulated to |a l | 2 Calculate the component a of each focal point according to equation (8). l Then, the a calculated from equation (8) l Substitute into equation (3) to calculate the complex amplitude CA of the light wave.

[0107] |CA′|=f1(|CA|) (4)

[0108] CA′=exp(iarg(CA))*|CA′| (5)

[0109]

[0110] |a l | 2 =f2(|a l ′| 2 (7)

[0111] al =exp(iarg(a l ′))*|a l | (8)

[0112] In equations (4) to (8), CA is the complex amplitude of the light wave, CA′ is the modulated complex amplitude of the light wave, and a l ′ is the modulated a l ,|a l | 2 Let |a| be the diffraction efficiency of the focal point with diffraction order l. l ′| 2 Let |a| be the diffraction efficiency at the focal point with modulated diffraction order l, || denotes the sign of the absolute value, i.e., |CA| is the absolute value of CA, |CA′| is the absolute value of CA′, and |a| is the absolute value of CA′. l | is for a l Take the absolute value, arg is the argument function, arg(a l ′) represents the phase of the focal point of the modulated diffraction order l; ρ = r 2 r is the radial distance from the center of the pupil; R is the design radius; λ is the wavelength of light; exp is the exponent symbol; i is the imaginary number symbol; W m The basic wavefront is l, which is the diffraction order at the focal point; f1 and f2 are the modulation functions. The expression for the modulation function f1 is shown in equation (10), and the expression for the modulation function f2 is shown in equation (11). Thus, the specific expressions for equations (4) and (7) are equations (10) and (11), respectively.

[0113] |CA′|=t1|CA|+(1-t1) (10)

[0114] |a l | 2 =t2|a l ′| 2 +(1-t2)|a ltarget | 2 (11)

[0115] In equations (10) to (11), t1 and t2 are modulation variables, t1 = 0.5 and t2 = 0.1, CA is the complex amplitude of the light wave, CA′ is the complex amplitude of the modulated light wave, || is the sign of the absolute value, and |a ltarget | 2 For the target diffraction efficiency at the focal point with diffraction order l, |a l | 2 Let |a| be the diffraction efficiency of the focal point with diffraction order l. l ′| 2 Let be the diffraction efficiency of the focal point with modulated diffraction order l.

[0116] Repeat the above steps continuously until the loop reaches 300 times. Approaching 1, and |a l |approaching|a ltarget The loop stops at this point.

[0117] ④ Based on the complex amplitude CA of the light wave corresponding to 300 cycles in step ③, determine the relationship between the wavefront of the light wave and the radial distance from the center of the pupil according to equation (9).

[0118]

[0119] In equation (9), E is the light wavefront of the final multifocal diffractometer, and CA is... Approaching 1 and |a l |approaching|a ltarget | The corresponding complex amplitude CA of the light wave (in this embodiment, it refers to the complex amplitude CA of the light wave after repeating step ③ 300 times), arg is the amplitude angle function, and λ is the wavelength of the light wave.

[0120] The final wavefront of the multifocal diffractometer obtained in this embodiment varies with the radial distance from the center of the pupil as follows: Figure 5 As shown, the wavefront of this light wave is smooth, without sharp edges or jumps. Figure 6 The diagram shows a comparison between the target diffraction efficiency at each focal point and the optimized diffraction efficiency of this embodiment. The optimized diffraction efficiency of this embodiment matches the target diffraction efficiency, and the total diffraction efficiency reaches 95%.

[0121] To examine the imaging quality of the multifocal diffractometer optimized in this embodiment, the areaMTF image quality function is used to represent the imaging quality [see Chen L, Singer B, Guirao A, Porter J, Williams DR. ImageMetrics for Predicting Subjective Image Quality. Optom Vis Sci. 2005; 82(5):358-69.]. A higher areaMTF value indicates better imaging quality. The imaging quality of the optimized multifocal diffractometer in this embodiment from object distances of -1D to 1D is as follows: Figure 7 As shown, three focal points were obtained at the set distances between the three objects.

[0122] Example 2

[0123] In this embodiment, the pupil radius of the person using the multifocal diffractometer is 3mm. Based on this pupil radius, the design radius R = 3mm is determined. According to the actual application requirements, the light wavelength λ = 550nm is determined. Taking this case as an example, the optimization algorithm of the multifocal diffractometer of the present invention is explained in detail, and the steps are as follows:

[0124] ① Based on practical application requirements, the number of focal points is determined to be 5, i.e., n=5. The diffraction order of each focal point is determined according to practical application requirements, and denoted as l, l=l1, l2,…,ln. Specifically, l1=-8, l2=-4, l3=0, l4=4, ln=l5=8. Simultaneously, the target diffraction efficiency |a| of the focal point with diffraction order l is determined according to practical application requirements. ltarget | 2 , specifically, |a -8 | 2 =0.36,|a -4 | 2 =0.09,|a0| 2 =0.18,|a4| 2 =0.09,|a8| 2 =0.27.

[0125] The refractive power φ of the fundamental wavefront can be calculated using equation (13). m =0.1225D (D is an abbreviation for diopters), based on the diffraction order of the five foci, from equation lφ m The refractive powers of the five focal points were calculated to be -0.98D, -0.49D, 0D, 0.49D, and 0.98D, respectively.

[0126]

[0127] In equation (13), R is the design radius, λ is the wavelength of light, and φ is the wavelength of light. m The refractive power of the base wavefront.

[0128] ② Randomly assign an initial phase arg(a) to each focus. l ), calculate the component a of each focal point according to equation (1) l Then, the complex amplitude CA of the light wave is calculated using equation (3).

[0129] a l =arg(a l )*|a ltarget | (1)

[0130]

[0131]

[0132] In equations (1) to (3), al It is a complex number, arg is the argument function, arg(a) l ) represents the phase of the focus with diffraction order l, |a ltarget | represents the target amplitude at the focal point with a diffraction order of l. |a ltarget | 2 Let be the target diffraction efficiency at the focal point with diffraction order l, || be the absolute value sign, arg be the argument function, exp be the exponent sign, i be the imaginary number sign, Wm be the fundamental wavefront, r be the radial distance from the center of the pupil, R be the design radius, λ be the wavelength of the light wave, and l be the diffraction order at the focal point.

[0133] ③ The phase restoration method is used to cyclically modulate the complex amplitude CA of the light wave and the component a at the focal point with diffraction order l. l and diffraction efficiency |a l | 2 The phase restoration method used in this embodiment is the error attenuation method, and the operation is as follows:

[0134] Modulate |CA| into |CA′| according to equation (4), combine arg(CA) and |CA′| into CA′ according to equation (5), and then calculate a according to equation (6). l ′, from equation (7) |a l ′| 2 Modulated to |a l | 2 Calculate the component a of each focal point according to equation (8). l Then, the a calculated from equation (8) l Substitute into equation (3) to calculate the complex amplitude CA of the light wave.

[0135] |CA′|=f1(|CA|) (4)

[0136] CA′=exp(iarg(CA))*|CA′| (5)

[0137]

[0138] |a l | 2 =f2(|a l ′| 2 (7)

[0139] a l =exp(iarg(a l ′))*|a l | (8)

[0140] In equations (4) to (8), CA is the complex amplitude of the light wave, CA′ is the modulated complex amplitude of the light wave, and a l ′ is the modulated al ,|a l | 2 Let |a| be the diffraction efficiency of the focal point with diffraction order l. l ′| 2 Let |a| be the diffraction efficiency at the focal point with modulated diffraction order l, || denotes the sign of the absolute value, i.e., |CA| is the absolute value of CA, |CA′| is the absolute value of CA′, and |a| is the absolute value of CA′. l | is for a l Take the absolute value, arg is the argument function, arg(a l ′) represents the phase of the focal point of the modulated diffraction order l; ρ = r 2 r is the radial distance from the center of the pupil; R is the design radius; λ is the wavelength of light; exp is the exponent symbol; i is the imaginary number symbol; W m The basic wavefront is l, which is the diffraction order at the focal point; f1 and f2 are the modulation functions. The expression for the modulation function f1 is shown in equation (10), and the expression for the modulation function f2 is shown in equation (11). Thus, the specific expressions for equations (4) and (7) are equations (10) and (11), respectively.

[0141] |CA′|=t1|CA|+(1-t1) (10)

[0142] |a l | 2 =t2|a l ′| 2 +(1-t2)|a ltarget | 2 (11)

[0143] In equations (10) to (11), t1 and t2 are modulation variables, t1 = 0.5 and t2 = 0.1, CA is the complex amplitude of the light wave, CA′ is the complex amplitude of the modulated light wave, || is the sign of the absolute value, and |a ltarget | 2 For the target diffraction efficiency at the focal point with diffraction order l, |a l | 2 Let |a| be the diffraction efficiency of the focal point with diffraction order l. l ′| 2 Let be the diffraction efficiency of the focal point with modulated diffraction order l.

[0144] Repeat the above steps continuously until the loop reaches 300 times. Approaching 1, and |a l |approaching|a ltarget The loop stops at this point.

[0145] ④ Based on the complex amplitude CA of the light wave corresponding to 300 cycles in step ③, determine the relationship between the wavefront of the light wave and the radial distance from the center of the pupil according to equation (9).

[0146]

[0147] In equation (9), W is the light wavefront of the final multifocal diffractometer, and CA is... Approaching 1 and |a l |approaching|a ltarget | The corresponding complex amplitude CA of the light wave (in this embodiment, it refers to the complex amplitude CA of the light wave after repeating step ③ 300 times), arg is the amplitude angle function, and λ is the wavelength of the light wave.

[0148] The relationship between the wavefront of the multifocal diffractometer and the radial distance from the center of the pupil obtained in this embodiment is as follows: Figure 8 As shown, the wavefront of this light wave is smooth, without sharp edges or jumps. Figure 9 The graph shows a comparison between the target diffraction efficiency at a single focus and the optimized diffraction efficiency of this embodiment. The optimized diffraction efficiency of this embodiment matches the target diffraction efficiency, and the total diffraction efficiency reaches 96%.

[0149] To examine the imaging quality of the multifocal diffractometer optimized in this embodiment, the areaMTF image quality function is used to represent the imaging quality. A higher areaMTF value indicates better imaging quality. The imaging quality of the optimized multifocal diffractometer from -1D to 1D object distances is shown below. Figure 10 As shown, five focal points were obtained at five set object distances.

[0150] Example 3

[0151] In this embodiment, the pupil radius of the person using the multifocal diffractometer is 3mm. Based on this pupil radius, the design radius R = 3mm is determined. According to the actual application requirements, the light wavelength λ = 550nm is determined. Taking this case as an example, the optimization algorithm of the multifocal diffractometer of the present invention is explained in detail, and the steps are as follows:

[0152] ① Based on practical application requirements, the number of focal points is determined to be 9, i.e., n=9. The diffraction order of each focal point is determined according to practical application requirements and denoted as l, l=l1, l2,…,ln. Specifically, l1=-8, l2=-6, l3=-4, l4=-2, l5=0, l6=2, l7=4, l8=6, ln=l9=8. Simultaneously, the target diffraction efficiency |a| of the focal point with diffraction order l is determined according to practical application requirements. ltarget | 2 , specifically, |a -8 |2 =|a -6 | 2 =|a -4 | 2 =|a -2 | 2 =|a0| 2 =|a2| 2 =|a4| 2 =|a6| 2 =|a8| 2 =0.11. The refractive power φ of the fundamental wavefront can be calculated from equation (13). m =0.1225D (D is an abbreviation for diopters), based on the diffraction order of the nine focal points, from equation lφ m The refractive powers of the nine focal points were calculated to be -0.98D, -0.74D, -0.49D, -0.25D, 0D, 0.25D, 0.49D, 0.74D, and 0.98D, respectively.

[0153]

[0154] In equation (13), R is the design radius, λ is the wavelength of light, and φ is the wavelength of light. m The refractive power of the base wavefront.

[0155] ② Randomly assign an initial phase arg(a) to each focus. l ), calculate the component a of each focal point according to equation (1) l Then, the complex amplitude CA of the light wave is calculated using equation (3).

[0156] a l =arg(a l )*|a ltarget | (1)

[0157]

[0158]

[0159] In equations (1) to (3), a l It is a complex number, arg is the argument function, arg(a) l ) represents the phase of the focus with diffraction order l, |a ltarget | represents the target amplitude at the focal point with a diffraction order of l. |a ltarget | 2 Let W be the target diffraction efficiency at the focal point with diffraction order l, || denotes the absolute value sign, arg denotes the argument function, exp denotes the exponent sign, i denotes the imaginary number sign, and W is the derivation of the target diffraction efficiency at the focal point with diffraction order l. mThe basic wavefront is defined as follows: r is the radial distance from the center of the pupil, R is the design radius, λ is the wavelength of the light wave, and l is the diffraction order at the focal point.

[0160] ③ The phase restoration method is used to cyclically modulate the complex amplitude CA of the light wave and the component a at the focal point with diffraction order l. l and diffraction efficiency |a l | 2 The phase restoration method used in this embodiment is the error attenuation method, and the operation is as follows:

[0161] Modulate |CA| into |CA′| according to equation (4), combine arg(CA) and |CA′| into CA′ according to equation (5), and then calculate a according to equation (6). l ′, from equation (7) |a l ′| 2 Modulated to |a l | 2 Calculate the component a of each focal point according to equation (8). l Then, the a calculated from equation (8) l Substitute into equation (3) to calculate the complex amplitude CA of the light wave.

[0162] |CA′|=f1(|CA|) (4)

[0163] CA′=exp(iarg(CA))*|CA′| (5)

[0164]

[0165] |a l | 2 =f2(|a l ′| 2 (7)

[0166] a l =exp(iarg(a l ′))*|a l | (8)

[0167] In equations (4) to (8), CA is the complex amplitude of the light wave, CA′ is the modulated complex amplitude of the light wave, and a l ′ is the modulated a l ,|a l | 2 Let |a| be the diffraction efficiency of the focal point with diffraction order l. l ′| 2 Let |a| be the diffraction efficiency at the focal point with modulated diffraction order l, || denotes the sign of the absolute value, i.e., |CA| is the absolute value of CA, |CA′| is the absolute value of CA′, and |a| is the absolute value of CA′. l | is for a lTake the absolute value, arg is the argument function, arg(a l ′) represents the phase of the focal point of the modulated diffraction order l; ρ = r 2 r is the radial distance from the center of the pupil; R is the design radius; λ is the wavelength of light; exp is the exponent symbol; i is the imaginary number symbol; W m The basic wavefront is f1 and f2 are the modulation functions. The expression of the modulation function f1 is shown in equation (10), and the expression of the modulation function f2 is shown in equation (11). Thus, the specific expressions of equations (4) and (7) are equations (10) and (11), respectively.

[0168] |CA′|=t1|CA|+(1-t1) (10)

[0169] |a l | 2 =t2|a l ′| 2 +(1-t2)|a l target | 2 (11)

[0170] In equations (10) to (11), t1 and t2 are modulation variables, t1 = 0.5 and t2 = 0.1, CA is the complex amplitude of the light wave, CA′ is the complex amplitude of the modulated light wave, || is the sign of the absolute value, and |a ltarget | 2 For the target diffraction efficiency at the focal point with diffraction order l, |a l | 2 Let |a| be the diffraction efficiency of the focal point with diffraction order l. l ′| 2 Let be the diffraction efficiency of the focal point with modulated diffraction order l.

[0171] Repeat the above steps continuously until the loop reaches 300 times. Approaching 1, and |a l |approaching|a ltarget The loop stops at this point.

[0172] ④ Based on the complex amplitude CA of the light wave corresponding to 300 cycles in step ③, determine the relationship between the wavefront of the light wave and the radial distance from the center of the pupil according to equation (9).

[0173]

[0174] In equation (9), W is the light wavefront of the final multifocal diffractometer, and CA is... Approaching 1 and |a l |approaching|a ltarget| The corresponding complex amplitude CA of the light wave (in this embodiment, it refers to the complex amplitude CA of the light wave after repeating step ③ 300 times), arg is the amplitude angle function, and λ is the wavelength of the light wave.

[0175] The relationship between the wavefront of the multifocal diffractometer and the radial distance from the center of the pupil obtained in this embodiment is as follows: Figure 11 As shown, the wavefront of this light wave is smooth, without sharp edges or jumps. Figure 12 The diagram shows a comparison between the target diffraction efficiency at each focal point and the optimized diffraction efficiency of this embodiment. The optimized diffraction efficiency of this embodiment matches the target diffraction efficiency, and the total diffraction efficiency reaches 98%.

[0176] To examine the imaging quality of the multifocal diffractometer optimized in this embodiment, the areaMTF image quality function is used to represent the imaging quality. A higher areaMTF value indicates better imaging quality. The imaging quality of the optimized multifocal diffractometer from -1D to 1D object distances is shown below. Figure 13 As shown, within the set object distance range, the image quality has begun to be maintained continuously, exhibiting the characteristics of continuous depth of field.

[0177] Example 4

[0178] In this embodiment, the pupil radius of the person using the multifocal diffractometer is 3mm. Based on this pupil radius, the design radius R = 3mm is determined. According to the actual application requirements, the light wavelength λ = 550nm is determined. Taking this case as an example, the optimization algorithm of the multifocal diffractometer of the present invention is explained in detail, and the steps are as follows:

[0179] ① Based on practical application requirements, the number of focal points is determined to be 9, i.e., n=9. The diffraction order of each focal point is determined according to practical application requirements and denoted as l, l=l1, l2,…,ln. Specifically, l1=-8, l2=-6, l3=-4, l4=-2, l5=0, l6=2, l7=4, l8=6, ln=l9=8. Simultaneously, the target diffraction efficiency |a| of the focal point with diffraction order l is determined according to practical application requirements. ltarget | 2 , specifically, |a -8 | 2 =|a -6 | 2 =|a -4 | 2 =|a -2 | 2 =|a0| 2 =|a2| 2 =|a4| 2 =|a6| 2 =|a8|2 =0.11.

[0180] The refractive power φ of the fundamental wavefront can be calculated using equation (13). m =0.1225D (D is an abbreviation for diopters), based on the diffraction order of the nine focal points, from equation lφ m The refractive powers of the nine focal points were calculated to be -0.98D, -0.74D, -0.49D, -0.25D, 0D, 0.25D, 0.49D, 0.74D, and 0.98D, respectively.

[0181]

[0182] In equation (13), R is the design radius, λ is the wavelength of light, and φ is the wavelength of light. m The refractive power of the base wavefront.

[0183] ② Randomly assign an initial phase arg(a) to each focus. l ), calculate the component a of each focal point according to equation (1) l Then, the complex amplitude CA of the light wave is calculated using equation (3).

[0184] a l =arg(a l )*|a ltarget | (1)

[0185]

[0186]

[0187] In equations (1) to (3), a l It is a complex number, arg is the argument function, arg(a) l ) represents the phase of the focus with diffraction order l, |a ltarget | represents the target amplitude at the focal point with a diffraction order of l. |a ltarget | 2 Let W be the target diffraction efficiency at the focal point with diffraction order l, || denotes the absolute value sign, arg denotes the argument function, exp denotes the exponent sign, i denotes the imaginary number sign, and W is the derivation of the target diffraction efficiency at the focal point with diffraction order l. m The basic wavefront is defined as follows: r is the radial distance from the center of the pupil, R is the design radius, λ is the wavelength of the light wave, and l is the diffraction order at the focal point.

[0188] ③ The phase restoration method is used to cyclically modulate the complex amplitude CA of the light wave and the component a at the focal point with diffraction order l. l and diffraction efficiency |a l | 2 The phase recovery method specifically used in this embodiment is the hybrid input-output method, and the operation is as follows:

[0189] S1, modulate |CA| into |CA′| according to equation (4), combine arg(CA) and |CA′| into CA′ according to equation (5), and then calculate a according to equation (6). l ′, from equation (7) |a l ′| 2 Modulated to |a l | 2 Calculate the component a of each focal point according to equation (8). l Then, the a calculated from equation (8) l Substitute into equation (3) to calculate the complex amplitude CA of the light wave.

[0190] |CA′|=f1(|CA|) (4)

[0191] CA′=exp(iarg(CA))*|CA′| (5)

[0192]

[0193] |a l | 2 =f2(|a l ′| 2 (7)

[0194] a l =exp(iarg(a l ′))*|a l | (8)

[0195] In equations (4) to (8), CA is the complex amplitude of the light wave, CA′ is the modulated complex amplitude of the light wave, and a l ′ is the modulated a l ,|a l | 2 Let |a| be the diffraction efficiency of the focal point with diffraction order l. l ′| 2 Let |a| be the diffraction efficiency at the focal point with modulated diffraction order l, || denotes the sign of the absolute value, i.e., |CA| is the absolute value of CA, |CA′| is the absolute value of CA′, and |a| is the absolute value of CA′. l | is for a l Take the absolute value, arg is the argument function, arg(a l ′) represents the phase of the focal point of the modulated diffraction order l; ρ = r 2 r is the radial distance from the center of the pupil; R is the design radius; λ is the wavelength of light; exp is the exponent symbol; i is the imaginary number symbol; W mThe basic wavefront is l, which is the diffraction order at the focal point; f1 and f2 are the modulation functions. The expression for the modulation function f1 is shown in equation (10), and the expression for the modulation function f2 is shown in equation (11). Thus, the specific expressions for equations (4) and (7) are equations (10) and (11), respectively.

[0196] |CA′|=t1|CA|+(1-t1) (10)

[0197] |a l | 2 =t2|a l ′| 2 +(1-t2)|a l target | 2 (11)

[0198] In equations (10) to (11), t1 and t2 are modulation variables, t1 = 0.5 and t2 = 0.1, CA is the complex amplitude of the light wave, CA′ is the complex amplitude of the modulated light wave, || is the sign of the absolute value, and |a ltarget | 2 For the target diffraction efficiency at the focal point with diffraction order l, |a l | 2 Let |a| be the diffraction efficiency of the focal point with diffraction order l. l ′| 2 Let be the diffraction efficiency of the focal point with modulated diffraction order l.

[0199] S2, repeat the operation of step S1, and after q cycles, the component a of the focal point with diffraction order l is obtained. l denoted as a lq The diffraction efficiency of a focal point with a diffraction order of l is denoted as |a''. lq ′| 2 If ||a lq ′| 2 -|a ltarget | 2 |<E0, where E0 is the target deviation and E0=0.005, then the component a of the focus with diffraction order l obtained in the qth cycle is... l Reverse compensation is performed according to formula (11).

[0200] Soon a lq Adjusted according to equation (12) Then the result obtained from equation (12) As a l Substitute into equation (3) to calculate the complex amplitude CA of the light wave.

[0201]

[0202] In equation (12), q is the number of cycles, and β = 0.001. Let be the amplitude of the focus with diffraction order l obtained in the (q-1)th cycle, i.e. The focal component a with diffraction order l obtained in the (q-1)th cycle l Take the absolute value, a lq ′ is the component a of the focus with diffraction order l obtained in the qth cycle. l , It is the amplitude of the focus with diffraction order l obtained in the qth cycle;

[0203] If ||a lq ′| 2 -|a ltarget | 2 |≥E0, where E0 is the target deviation, and E0=0.005, then it is not necessary to follow equation (11) for the component a of the focal point with diffraction order l. l Perform reverse compensation and continue the loop of step S1;

[0204] The operation of steps S1 and S2 is repeated continuously until the number of iterations reaches 1000. Approaching 1, and |a l |approaching|a ltarget The loop stops at this point.

[0205] ④ Based on the complex amplitude CA of the light wave corresponding to 1000 cycles in step ③, determine the relationship between the light wave wavefront and the radial distance from the center of the pupil according to equation (9).

[0206]

[0207] In equation (9), w is the light wavefront of the final multifocal diffractometer, and CA is... Approaching 1 and |a l |approaching|a ltarget | The corresponding complex amplitude CA of the light wave (in this embodiment, it refers to the complex amplitude CA of the light wave after repeating step ③ 1000 times), arg is the amplitude angle function, and λ is the wavelength of the light wave.

[0208] The relationship between the wavefront of the multifocal diffractometer and the radial distance from the center of the pupil obtained in this embodiment is as follows: Figure 14 As shown, the wavefront of this light wave is smooth, without sharp edges or jumps. Figure 15 The diagram shows a comparison between the target diffraction efficiency at each focal point and the optimized diffraction efficiency of this embodiment. The optimized diffraction efficiency of this embodiment matches the target diffraction efficiency, and the total diffraction efficiency reaches 99%.

[0209] To examine the imaging quality of the multifocal diffractometer optimized in this embodiment, the areaMTF image quality function is used to represent the imaging quality. A higher areaMTF value indicates better imaging quality. The imaging quality of the optimized multifocal diffractometer from -1D to 1D object distances is shown below. Figure 16 As shown, within the set object distance range, the image quality has begun to be maintained continuously, exhibiting the characteristics of continuous depth of field.

Claims

1. An optimization algorithm for a multifocal diffractometer, characterized in that, Includes the following steps: ① Determine the number of focal points, the diffraction order of each focal point, and the target diffraction efficiency of each focal point based on actual application requirements. Let the number of focal points be denoted as n, where n is an integer and n≥2. Let the diffraction order of each focal point be denoted as l, where l=l1,l2,…,ln, and l1,l2,…,ln are distinct integers. Let the target diffraction efficiency of the focal point with diffraction order l be denoted as |a l tar get | 2 ; ② Randomly assign an initial phase arg(a) to each focus. l ), calculate the component a of each focal point according to equation (1) l Then, the complex amplitude CA of the light wave is calculated using equation (3). am l Arg(a l )*|a l target | (1) In equations (1) to (3), a l It is a complex number, arg is the argument function, arg(a) l ) represents the phase of the focus with diffraction order l, |a l target | represents the target amplitude at the focal point with diffraction order l, | represents the absolute value sign, arg is the argument function, exp is the exponent sign, i is the imaginary sign, and W m The basic wavefront is defined as follows: r is the radial distance from the center of the pupil, R is the design radius, λ is the wavelength of the light wave, and l is the diffraction order at the focal point. ③ The phase restoration method is used to cyclically modulate the complex amplitude CA of the light wave and the component a at the focal point with diffraction order l. l and diffraction efficiency |a l | 2 ,Right now, S301, according to equation (4), |CA| is modulated into |CA'|, arg(CA) and |CA'| are combined into CA' according to equation (5), and then a is calculated according to equation (6). l ', from equation (7) |a l '| 2 Modulated to |a l | 2 Calculate the component a of each focal point according to equation (8). l Then, the a calculated from equation (8) l Substitute into equation (3) to calculate the complex amplitude CA of the light wave. |CA'|=f1(|CA|) (4) CA'=exp(i arg(CA))*|CA'| (5) |a l | 2 =f2(|a l '| 2 ) (7) a l =exp(iarg(a l '))*|a l | (8) In equations (4) to (8), CA is the complex amplitude of the light wave, CA' is the modulated complex amplitude of the light wave, and a l 'is the modulated a' l ,|a l | 2 Let |a| be the diffraction efficiency of the focal point with diffraction order l. l '| 2 Let be the diffraction efficiency at the focal point with modulated diffraction order l, || denotes the absolute value sign, arg is the argument function, and arg(a) l ') represents the phase of the focal point of the modulated diffraction order l; ρ = r 2 r is the radial distance from the center of the pupil; R is the design radius; λ is the wavelength of light; exp is the exponent symbol; i is the imaginary number symbol; W m The fundamental wavefront is l, which is the diffraction order at the focal point; f1 and f2 are the modulation functions. S302, continue the operation of step S301 in a loop until... Approaching 1 and |a l |approaching|a l target |; ④ Repeat step ③ until... Approaching 1 and |a l |approaching|a l target The complex amplitude CA of the light wave corresponding to the time is determined according to equation (9), which shows the relationship between the light wave wavefront and the radial distance from the center of the pupil. In equation (9), W is the wavefront of the final multifocal diffractometer, and CA is... Approaching 1 and |a l |approaching|a l target | The corresponding complex amplitude CA of the light wave at time |, arg is the amplitude angle function, and λ is the wavelength of the light wave; Step ③ describes a phase restoration method that includes at least one of the following: error attenuation method and hybrid input / output method. In the error attenuation method and the hybrid input / output method, the expression for the modulation function f1 is shown in equation (10), and the expression for the modulation function f2 is shown in equation (11). |CA'|=t1|CA|+(1-t1) (10) |a l | 2 =t2|a l '| 2 +(1-t2)|a l target | 2 (11) In equations (10) to (11), t1 and t2 are modulation variables, t1 is 0 to 1, t2 is 0 to 1, CA is the complex amplitude of the light wave, CA' is the complex amplitude of the modulated light wave, || is the sign of taking the absolute value, and |a l target | 2 For the target diffraction efficiency at the focal point with diffraction order l, |a l | 2 Let |a| be the diffraction efficiency of the focal point with diffraction order l. l '| 2 The diffraction efficiency of the focal point with modulated diffraction order l; The operation steps of the mixed input / output method are as follows: S3011, perform a loop according to the operation in step S301. After q loops of step S301, the component a of the focus with diffraction order l l is denoted as a lq ', and the diffraction efficiency of the focus with diffraction order l is denoted as |a lq '| 2 . If ||a lq '| 2 - |a l target | 2 | < E0, where E0 is the target deviation, then perform reverse compensation on the component a of the focus with diffraction order l obtained in the q-th loop according to Equation (11). l ​ Soon a lq Adjusted according to formula (12) Then the result obtained from equation (12) As a l Substitute into equation (3) to calculate the complex amplitude CA of the light wave. In equation (12), q is the number of iterations, 0 < β ≤ 1. Let a be the amplitude of the focus of the diffraction order l obtained in the (q-1)th cycle. lq 'The component a of the focal point with diffraction order l obtained in the qth cycle. l , It is the amplitude of the focus with diffraction order l obtained in the qth cycle; If ||a lq '| 2 -|a l target | 2 If |≥E0, and E0 is the target deviation, then it is not necessary to apply equation (11) to the component a of the focal point with diffraction order l. l Perform reverse compensation; S3012, continue the operation of step S3011 in a loop until... Approaching 1 and |a l |approaching|a l target | 2. The optimization algorithm for the multifocal diffractometer according to claim 1, characterized in that, The target deviation E0 ranges from 0 to 0.

05.

3. The optimization algorithm for the multifocal diffractometer according to claim 1 or 2, characterized in that, The Approaching 1 means It is between 0.75 and 1.

4. The optimization algorithm for the multifocal diffractometer according to claim 1 or 2, characterized in that, The design radius R is equal to or not equal to the pupil radius of the person using the multifocal diffractometer.

5. The optimization algorithm for the multifocal diffractometer according to claim 4, characterized in that, The design radius R is 1.0 to 1.5 times the pupil radius of the person using the multifocal diffraction lens.

6. The optimization algorithm for the multifocal diffractometer according to claim 1 or 2, characterized in that, As the number of focal points gradually increases, the imaging quality of the diffraction mirror designed by this optimization algorithm gradually exhibits the characteristics of continuous depth of field.

7. The optimization algorithm for the multifocal diffractometer according to claim 1 or 2, characterized in that, This optimization algorithm is applicable to the design of multifocal diffractors used by the human eye, or to the design of multifocal diffractors in optical systems.

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