CN104793336B - A kind of design of diffractive optical element method suitable for multi-wavelength - Google Patents
A kind of design of diffractive optical element method suitable for multi-wavelength Download PDFInfo
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Abstract
The invention discloses a kind of design of diffractive optical element method suitable for multi-wavelength, 1) determines the wavelength and the corresponding optical field distribution of each wavelength laser of design of diffractive optical element laser；2) the corresponding target image of each wavelength and image-forming range are determined；3) overall dimensions and phase place exponent number of diffraction optical element are determined；4) according to the corresponding target image of each wavelength, the Single wavelength diffraction element suitable for each wavelength is separately designed using GS algorithms；5) take out step 4) in the corresponding diffraction element height of the most long wavelength that obtains as elemental height, add certain height on diffraction element each pixel；6) by step 5) in the equivalent phase Single wavelength diffraction element corresponding with each wavelength of each pixel structure height correspondence each wavelength after adjustment make the difference in the equivalent phase of the pixel；7) repeat step 5) and step 6), when each wavelength poor quadratic sum of correspondence is minimum, iteration is completed；8) phase place that design is obtained is quantified.
Description
Technical field
The invention belongs to Application Optics field, more particularly to a kind of design of diffractive optical element for being employed flexibly for multi-wavelength
Method.
Background technology
Diffraction optical element (Diffractive optical elements, DOE) is that a kind of diffraction based on light wave is managed
By the device for growing up, the characteristics of with not available for traditional optical elements, be greatly promoted optical system miniaturization,
Integrated and array, improves and laser machines the neck such as improved efficiency in laser facula shaping, facula correction, beam quality
Domain is widely used.
Traditional DOE operation wavelengths are single, greatly limit its use range.1978, Dammann proposed color for the first time
Coloured light separates the concept of phase board, and different light is isolated to different diffraction times with the success of one piece of phase-plate only, but only
Only it is that simply light is separated, imaging is not studied.Subsequently, domestic and international researcher is to multi-wavelength diffraction unit
Part has carried out correlative study, and Doskolovich, L.L. determine the depth of each step of diffraction element structure by wavelength ratio
Degree, then be iterated by each face face type error, achievement realizes the separate imaging of simple light field, but due to step depth
It is non-linear, it is unfavorable for processing and makes；Bengtsson proposes a kind of by input face and the algorithm of output face discretization, is ensureing
On the premise of step depth is linear, two wavelength are realized on certain distance into specific picture；Subsequently Yusuke Ogura are at which
On the basis of, the weight in algorithm is optimized, the diffraction element design of multi-wavelength separate imaging is realized, the method is beneficial to
Processing, but the image points for obtaining are limited, and the distance of its output light field is shorter；Xuegong Deng and Ray T.Chen
On the basis of Single wavelength GS algorithms using the cascade of two diffraction elements mode, to the flat of the imaging of different wave length in addition weight
Weighing apparatus, realizes the separation of multi-wavelength and focuses on, and this method cannot realize practicality in practice due to the restriction of alignment error
Change.
Based on above present situation, the present invention proposes a kind of method for designing of multi-wavelength diffraction element, and the method is mainly in list
On the basis of wavelength DOE designs, an optimum organization is highly carried out to the Single wavelength DOE of each wavelength, has been allowed to form applicable
In the diffraction element structure of multiple wavelength.The method is not limited by wavelength and points, it is only necessary to a diffraction element, you can
Far field forms color colored light field true to nature.
The content of the invention
The technical problem to be solved in the present invention is：When overcoming multi-wavelength diffraction element to design, output light field is simple, export away from
From short problem.A kind of new Iterative Design method is proposed, by multi-wavelength diffraction element being found with each Single wavelength diffraction unit
The point of the equivalent phase difference minimum of part, calculates the multi-wavelength diffraction element phase height of optimum, realizes desin speed same soon
When can guarantee that the diffraction element design of higher diffraction efficiency and relatively low root-mean-square error.
The present invention solve the technical scheme that adopts of above-mentioned technical problem for：A kind of diffraction optical element generated for image
Method for designing, design procedure are as follows：
Step (1), the wavelength (λ for determining laser used in design of diffractive optical element1、λ2、λ3…λn) and each wavelength swash
Corresponding optical field distribution (the U of light1、U2、U3…Un)；
Step (2), according to specific needs, determines that the corresponding target image of each wavelength is distributed (A1、A2、A3…An) and imaging
Apart from z；
Step (3), the overall dimensions L and phase place exponent number q that according to specific needs, determine diffraction element；
Step (4), according to the corresponding target image of each wavelength, separately design the unicast suitable for each wavelength using GS algorithms
The Single wavelength diffraction element that design is completed highly is designated as h by long diffraction element1、h2、h3…hn；Diffraction element height h and phase place
Relation such as formula (1) shown in；
The most long wavelengths obtained in step (5), taking-up step (4)1Corresponding diffraction element height as elemental height,
Certain height is added on diffraction element each pixel；
In formula (2), m is the integer in the range of [0, M], and M is arbitrary integer, and △ is the controllable factor of face type adjustment, is taken
Value scope is [- δ %, δ %], and δ is any real number more than 0 and less than 100, and h is multi-wavelength diffraction element height, (x, y) generation
The coordinate position of each pixel of table diffraction element, when adding m λ/(n-1) on Single wavelength DOE height, refractive indexes of the n for material, its
The integral multiple for changing into 2 π to the amount of phase modulation of wavelength X, imaging will not be affected, and add the height of △ λ/(n-1)
Degree, can make imaging produce center zero level, but when △ is in certain face type disparity range, center zero order intensity can be ignored, ripple
The light beam imaging of a length of λ meets imaging needs；
Step (6), by the equivalent phase of each pixel structure height correspondence each wavelength after adjustment in step (5) with
The corresponding Single wavelength diffraction element of each wavelength makes the difference in the equivalent phase of the pixel and is designated as RMS1、RMS2、RMS3、…RMSn；
Wherein, RMSk(k=1,2,3...n) is λ for the structure and wavelength after iterationkSingle wavelength diffraction element structure etc.
Effect difference；modaB () is MOD functions of the b to a.nk(k=1,2,3 ... n) is material to wavelength XkRefractive index；
Step (7), repeat step (5) and step (6), when the poor quadratic sum of each wavelength correspondence is minimum, iteration is completed, and is put down
Under side and definition such as (4)：
The m for obtaining and △ substitutes into the height that formula (2) is obtained each pixel of multi-wavelength DOE；
After step (8), iteration terminate, q rank quantizations, the phase place after quantization point are carried out to the phase distribution of input plane light field
Cloth, as final diffraction optical element phase distribution.
Wherein, the LASER Light Source u (x in the step (1)o,yo) it is Gaussian Profile.
Wherein, the target image in the step (2) is two dimensional image and parallel to diffraction element place plane, in image
The heart and element central line are vertical with element plane.
Wherein, the diffraction element phase place exponent number in the step (3) can only take 2n, n is integer.
Wherein, the u (x in the step (4)o,yo)、u1(x1,y1) and A (x1,y1) design when be all m × m point
Matrix, can adopt fresnel diffraction formula or Fu Langhe fraunhofer-diffraction formula to be calculated in GS algorithms.
Wherein, in the step (5) when being adjusted to height, adjusting range is selective.
Wherein, each wavelength is combined by the step (6) by equivalent phase, by the right of multi-wavelength diffraction element
The difference of the equivalent phase of each wavelength and the equivalent phase of the Single wavelength diffraction element of each wavelength is being iterated.
Wherein, the step (7) is by observation when the quadratic sum of the corresponding equivalent phase difference of each wavelength is minimum, repeatedly
In generation, completes；Actual conditions can also be had more and add weight, be judged using weighted sum of squares.
Present invention advantage compared with prior art is：
(1) instant invention overcomes the diffraction element of traditional multi-wavelength diffraction element method for designing design gained cannot be processed
Shortcoming, the structure after the method quantifies still has good imaging effect, can be used for reality processing, solve at present for
The problem that multi-wavelength diffraction element cannot be processed；
(2), compared with traditional design algorithm, not by counting and distance is limited, being imaged light field can be simple for output field for the present invention
Can be complicated, the step depth linear distribution of the structure after quantization a, it is only necessary to diffraction element, you can realize to multiple wavelength
Light beam is regulated and controled.
Description of the drawings
Fig. 1 is the flow chart of the design of diffractive optical element method for multi-wavelength；
Fig. 2 is the target image for diffraction element design, wherein, (a) wavelength X1Target field；(b) wavelength X2Target
；(c) wavelength X3Target field；(d) general objective field；
Fig. 3 is that the picture that the present invention diffraction element that obtains of design does not quantify phase distribution and carries out obtained by computer simulation is put down
Face optical field distribution, wherein, (a) wavelength X1Simulation light field of the light beam through DOE；(b) wavelength X2Simulation light field of the light beam through DOE；
(c) wavelength X3Light beam through DOE simulation light field；Simulation light field of (d) mixed light beam through DOE；
Fig. 4 is that the diffraction element quantization phase distribution that present invention design is obtained carries out the image plane obtained by computer simulation
Optical field distribution, wherein, (a) wavelength X1Simulation light field of the light beam through DOE；(b) wavelength X2Simulation light field of the light beam through DOE；
(c) wavelength X3Light beam through DOE simulation light field；Simulation light field of (d) mixed light beam through DOE；
Fig. 5 is the phase distribution when diffraction element that present invention design is obtained does not quantify；
Fig. 6 is the phase distribution after the diffraction element that present invention design is obtained quantifies.
Specific embodiment
Below in conjunction with the accompanying drawings and specific embodiment is discussed in detail the present invention.But below example is only limitted to explain this
Bright, protection scope of the present invention should include the full content of claim, and pass through following examples those skilled in the art
The full content of the claims in the present invention can be realized.
Embodiment：
Diffraction element design process for three wavelength is as follows：
Step (1), the wavelength (λ for determining laser used in design of diffractive optical element1=632nm, λ2=546.1nm,
λ3=435.8nm) and the corresponding light field of each wavelength laser be planar light；
Step (2), design object field are figure2 Shown colored magic square image, figure2 A () is wavelength X1Corresponding target
, figure2 B () is wavelength X2Corresponding target field, figure2 C () is wavelength X3Corresponding target field, image-forming range 70cm；
Step (3), the overall dimensions 4mm*4mm of diffraction element and phase place exponent number are 16；
Step (4), according to the corresponding target image of each wavelength, separately design the unicast suitable for each wavelength using GS algorithms
The Single wavelength diffraction element that design is completed highly is designated as h by long diffraction element1、h2、h3…hn；Diffraction element height h and phase place
Relation such as formula (9) shown in；
The most long wavelengths obtained in step (5), taking-up step (4)nCorresponding diffraction element height as elemental height,
Certain height is added on diffraction element each pixel；
In formula (10), m is the integer in the range of [0, M], and M is arbitrary integer, and △ is the controllable factor of face type adjustment, is taken
Value scope is [- δ %, δ %], and δ is any real number more than 0 and less than 100, and h is multi-wavelength diffraction element height, (x, y) generation
The coordinate position of each pixel of table diffraction element.When adding m λ/(n-1) on Single wavelength DOE height, its phase place to wavelength X is adjusted
The integral multiple for changing into 2 π of amount processed, imaging will not be affected.Plus the height of △ λ/(n-1), produce can imaging
Center zero level, but when △ is in certain face type disparity range, center zero order intensity can be ignored, and wavelength is imaged for the light beam of λ
Meet imaging needs.
Step (6), by the equivalent phase of each pixel structure height correspondence each wavelength after adjustment in step (5) with
The corresponding Single wavelength diffraction element of each wavelength makes the difference in the equivalent phase of the pixel and is designated as RMS1、RMS2、RMS3、…RMSn, such as
Shown in formula (11)；
Wherein, RMSk(k=1,2,3) are λ for the structure and wavelength after iterationkThe equivalent difference of Single wavelength diffraction element structure
Value；modaB () is MOD functions of the b to a.nk(k=1,2,3) it is material to wavelength XkRefractive index.
Step (7), repeat step (5) and step (6), when the poor quadratic sum of each wavelength correspondence is minimum, iteration is completed.It is flat
Under side and definition such as (12)：
The m for obtaining and △ substitutes into the height that formula (10) is obtained each pixel of multi-wavelength DOE.Obtain as shown in Figure 5
Diffraction optical element phase distribution, computer simulation is carried out to the phase distribution shown in Fig. 5 image field as shown in Figure 3 is obtained
Output.
After step (8), iteration terminate, 16 rank quantizations, the phase place after quantization are carried out to the phase distribution of input plane light field
Distribution, obtains phase distribution as shown in Figure 6 and carries out computer simulation to the phase distribution shown in Fig. 6 being obtained as shown in Figure 4
Image field output.
What the present invention was not elaborated partly belongs to techniques known.
Claims (9)
1. a kind of design of diffractive optical element method suitable for multi-wavelength, it is characterised in that the method overcomes multi-wavelength diffraction
When element is designed, output light field is simple, exports apart from short problem, by finding multi-wavelength diffraction element and each Single wavelength diffraction
The point of the equivalent phase difference minimum of element, calculates the multi-wavelength diffraction element phase height of optimum, realizes desin speed fast
The diffraction element design of higher diffraction efficiency and relatively low root-mean-square error, the design step of the diffraction element are can guarantee that simultaneously
It is rapid as follows：
Step (1), the wavelength (λ for determining laser used in design of diffractive optical element1、λ2、λ3…λn) and each wavelength laser pair
Optical field distribution (the U for answering1、U2、U3…Un)；
Step (2), according to specific needs, determines that the corresponding target image of each wavelength is distributed (A1、A2、A3…An) and image-forming range z；
Step (3), the overall dimensions L and phase place exponent number q that according to specific needs, determine diffraction element；
Step (4), according to the corresponding target image of each wavelength, the Single wavelength separately designed suitable for each wavelength using GS algorithms is spread out
Element is penetrated, the Single wavelength diffraction element that design is completed highly is designated as into h1、h2、h3…hn；Diffraction element height h and phase placePass
System is as shown in formula (1)；
The most long wavelengths obtained in step (5), taking-up step (4)1Corresponding diffraction element height as elemental height, in diffraction
Certain height is added on element each pixel；
In formula (2), m is the integer in the range of [0, M], and M is arbitrary integer, and △ is the controllable factor of face type adjustment, value model
Enclose for [- δ %, δ %], δ is any real number more than 0 and less than 100, and h is multi-wavelength diffraction element height, and (x, y) is represented and spread out
The coordinate position of each pixel of element is penetrated, when adding m λ/(n-1) on Single wavelength DOE height, refractive indexes of the n for material, which is to ripple
The integral multiple for changing into 2 π of the amount of phase modulation of long λ, imaging will not be affected, and add the height of △ λ/(n-1), meeting
Make imaging produce center zero level, but when △ is in certain face type disparity range, center zero order intensity can be ignored, and wavelength is λ
Light beam imaging meet imaging needs；
Step (6), equivalent phase and each ripple that each the pixel structure height after adjustment in step (5) is corresponded to each wavelength
The corresponding Single wavelength diffraction element of length makes the difference in the equivalent phase of the pixel and is designated as RMS1、RMS2、RMS3、…RMSn；
Wherein, RMSk(k=1,2,3...n) is λ for the structure and wavelength after iterationkThe equivalent difference of Single wavelength diffraction element structure
Value；modaB () is MOD functions of the b to a, nk(k=1,2,3 ... n) is material to wavelength XkRefractive index；
Step (7), repeat step (5) and step (6), when the poor quadratic sum of each wavelength correspondence is minimum, iteration is completed, quadratic sum
Under definition such as (4)：
The m for obtaining and △ substitutes into the height that formula (2) is obtained each pixel of multi-wavelength DOE；
After step (8), iteration terminate, q rank quantizations are carried out to the phase distribution of input plane light field, the phase distribution after quantization,
As final diffraction optical element phase distribution；
The shortcoming that the diffraction element of traditional multi-wavelength diffraction element method for designing design gained cannot be processed is the method overcomed,
Structure after the method quantifies still has good imaging effect, can be used for reality processing, solves at present for multi-wavelength
The problem that diffraction element cannot be processed；
The method output field not by counting and distance is limited, imaging light field can simply can be complicated, the step of the structure after quantization
Depth linear distribution a, it is only necessary to diffraction element, you can realize regulating and controlling the light beam of multiple wavelength.
2. a kind of design of diffractive optical element method suitable for multi-wavelength according to claim 1, it is characterised in that：Institute
It is Gauss light or planar light to state the LASER Light Source in step (1).
3. a kind of design of diffractive optical element method suitable for multi-wavelength according to claim 1, it is characterised in that：Institute
Stating the target image in step (2) is two dimensional image and connects parallel to diffraction element place plane, picture centre and element central
Line is vertical with element plane.
4. a kind of design of diffractive optical element method suitable for multi-wavelength according to claim 1, it is characterised in that：Institute
The diffraction element phase place exponent number stated in step (3) can only take 2n, n is integer.
5. a kind of design of diffractive optical element method suitable for multi-wavelength according to claim 1, it is characterised in that：Institute
State the u (x in step (4)o,yo)、u1(x1,y1) and A (x1,y1) design when be all m × m point matrix, can in GS algorithms
Calculated using fresnel diffraction formula or Fu Langhe fraunhofer-diffraction formula.
6. a kind of design of diffractive optical element method suitable for multi-wavelength according to claim 1, it is characterised in that：Institute
State in step (5) when being adjusted to height, according to specific application requirement and processing request, to M and δ values, so as to true
The span of fixed each parameter.
7. a kind of design of diffractive optical element method suitable for multi-wavelength according to claim 1, it is characterised in that：Institute
State step (6) to combine each wavelength by equivalent phase, by the equivalent phase to each wavelength of multi-wavelength diffraction element
Position is iterated with the difference of the equivalent phase of the Single wavelength diffraction element of each wavelength.
8. a kind of design of diffractive optical element method suitable for multi-wavelength according to claim 1, it is characterised in that：Institute
It is that iteration is completed when the quadratic sum of the corresponding equivalent phase difference of each wavelength is minimum to state step (7)；Also dependent on actual conditions plus
Enter weight, judged using weighted sum of squares.
9. a kind of design of diffractive optical element method suitable for multi-wavelength according to claim 1, it is characterised in that：Institute
It is to carry out 2 to the result for designing to state step (8)nIndividual step quantifies, and the height of each step is linear relationship.
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| CN110824721B (en) * | 2019-09-24 | 2021-11-23 | 杭州驭光光电科技有限公司 | Method for designing diffractive optical element and diffractive optical element |
| CN111679427A (en) * | 2020-06-19 | 2020-09-18 | 中南大学 | Optical imaging element design method, manufacturing method and optical imaging element thereof |
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