CN201107422Y - Isocandela beam-splitting grating for eliminating diffraction spectrum point - Google Patents

Abstract

The utility model relates to an isocandela light-splitting grating for suppressing zero order diffraction spectral points, the structure of which is a minisized periodically repeated zero order-suppressing dammann grating. In each period of the grating, the mirror symmetry of phase catastrophe points is based on the perpendicular bisector of the period, a phase value between the two neighboring phase catastrophe points of the second half period drifts relative to a phase value between neighboring phase catastrophe points corresponding to the first half period for Pi, the intensity of high order diffractive lights is equal, that is, I plus or minus 1 equal to I plus or minus 2 equal to equal to I plus or minus N, wherien, N is a positive integer larger than 1, the light-splitting ratio of the grating is 2N, and the parameters of the grating apply a fast drop algorithm and are optimized and calculated by a computer program: the number (K) of the phase catastrophe points, a phase value (Theta k) from the k minus 1th phase catastrophe point to the kth phase catastrophe point and the normalized coordinate value (xk) of the kth phase catastrophe point, and wherein, k is equal to 1, 2, to, K. In a distant field, the grating of the utility model obtains multi-beam outputs distributed in a non-zero order diffraction isocandela array with light-splitting ratios of 1 multiplied by 2, 1 multiplied by 4, 1 multiplied by 6, and so on.

Description

Eliminate the isocandela beam-splitting optical grating of Zero-order diffractive spectrum point

Technical field

This patent relates to the diffraction optics components and parts, particularly a kind of isocandela beam-splitting optical grating of eliminating Zero-order diffractive spectrum point, it is zero suppression level Darman raster, it can realize the monochromatic optical wave of single plane incident is divided into some isocandelas distributions in the far field, and under the situation of no foozle, eliminate Zero-order diffractive spectrum point fully.

Background technology

In numerous technical fields such as optical fiber communication, photometry calculation, Flame Image Process and optical disc storage, often require the input of single signal is transformed into the output of many signals, the optical beam splitting device can be realized above-mentioned requirements.The method that realizes optical beam-splitter is a lot, Darman raster (H.Dammann and K.Gortler based on the Fraunhofer diffraction principle design, " High-efficiency in-line multiple imagining by multiplephase holograms; " Opt.Commun.3,312-3151971) because of the efficient height, the beam distribution homogeneity is not subjected to advantages such as incident intensity distribution influence to become one of the most effective beam splitting device at present.

For Darman raster, the computing formula form of the computing formula of Zero-order diffractive level time light intensity and other order of diffraction time is different fully, and this causes when phase error occurring, and the variation of Zero-order diffractive hot spot relative theory value is also different with the inferior situation of other order of diffraction.For even number point Darman raster, Zhou Changhe points out by computer simulation, under the situation of not considering the Zero-order diffractive spectrum, the homogeneity of other diffraction spectra is not subjected to the influence of phase error, the Zero-order diffractive light intensity is only by phase error decision (C.Zhou etc. " Numerical study ofDammann array illuminators ", Appl.Opt.34,5961-5969,1995), this point is equally applicable to zero suppression level Darman raster.Rick L.Morrison in 1992 proposes the symmetrical method of utilization and reduces the difficulty in computation (R.L.Morrison that grating parameter is optimized, " Symmetries that simplify the design ofspot-array phase gratings; " J.Opt.Soc.Am.A 9,464-471,1992), and interior phase jump point mirror of the cycle of having mentioned is to symmetry, the structure of front and back semiperiod position phase phase difference of pi, but Morrison does not further point out this structure and can eliminate the Zero-order diffractive spectrum under the situation of no foozle, do not provide its numerical solution yet.

Summary of the invention

The technical problems to be solved in the utility model is to provide a kind of isocandela beam-splitting optical grating of eliminating Zero-order diffractive spectrum point, this grating is eliminated the Zero-order diffractive spectrum fully under the situation of no foozle, obtain corresponding to 1 * 2 in the far field, 1 * 4,1 * 6 ... the multiple beam that distributes of the isocandela spot array of no center Zero-order diffractive light intensity.

Technical solution of the present utility model is as follows:

A kind of isocandela beam-splitting optical grating of eliminating Zero-order diffractive spectrum point, the structure that is characterized in this grating is the zero suppression level Darman raster that a microstructure periodically repeats, in each cycle of grating, phase jump point is about the perpendicular bisector mirror image symmetry in this cycle, position between the two-phase ortho position phase catastrophe point in later half cycle is worth mutually with respect to the position phase value drift π between the phase jump point of preceding semiperiod correspondence, each senior diffraction light light intensity is equal, i.e. I _{± 1}=I _{± 2}=...=I _±, wherein N is the positive integer greater than 1, and the splitting ratio of this grating is 2N, and the parameter of this grating adopts quick descent algorithm and appliance computer program optimization to calculate: the number K of SPA sudden phase anomalies point, k-1 are worth θ to k position between mutually mutually _kWith k phase jump point normalization coordinate figure x _k, wherein k be 1,2 ... K.

Position between the described phase jump point is many-valued mutually, and the parameter of described grating adopts quick descent algorithm to calculate by following formula and appliance computer program optimization:

$\left\{\begin{array}{c}A\left(0\right)=0\\ A\left(n\right)=\left(\frac{1}{\mathrm{n\π}}\right)\×(\underset{k=1}{\overset{K}{\mathrm{\Σ}}}-(\cos \left({\mathrm{\α}}_k\right)-\cos \left({\mathrm{\α}}_{k-1}\right)\left)\sin \right({\mathrm{\θ}}_k)+i\underset{k=1}{\overset{K}{\mathrm{\Σ}}}(\cos \left({\mathrm{\α}}_k\right)-\cos \left({\mathrm{\α}}_{k-1}\right)\left)\cos \right({\mathrm{\θ}}_k\left)\right)\end{array}\right.$

In the formula: in the formula: α _k=2 π n _x, n is that the order of diffraction is inferior, K is the number of SPA sudden phase anomalies point, x _kBe k phase jump point, θ _kBe k-1 to k position between mutually value mutually, light distribution is I (n)=A (n) A ^*(n).

Position between the described phase jump point is 0 mutually, and π is alternate, and the parameter of described grating adopts quick descent algorithm to calculate by following formula and appliance computer program optimization:

$\left\{\begin{array}{c}A\left(0\right)=0\\ A\left(n\right)=\left(\frac{1}{\mathrm{n\π}}\right)\×\left(\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\right(-1{)}^k\left(\cos \right({\mathrm{\α}}_k)-\cos ({\mathrm{\α}}_{k-1}\left)\right)\end{array}\right.$

In the formula: α _k=2 π nx _k, n is that the order of diffraction is inferior, K is the number of SPA sudden phase anomalies point, x _kBe k phase jump point, θ _kBe k-1 to k position between mutually value mutually, light distribution is I (n)=A (n) A ^*(n).

The manufacture method of the isocandela beam-splitting optical grating of described elimination zero level comprises the following steps:

1. according to beam splitting number of spots=2N, the splitting ratio of the selected zero suppression level Darman raster that need make is 2N, can only get even number;

2. adopt quick descent algorithm and appliance computer program optimization to calculate the number K of the SPA sudden phase anomalies point of the two-value position Darman raster of zero suppression level mutually, k-1 and be worth θ mutually between mutually to k position _kWith k phase jump point normalization coordinate figure x _k

3. according to the grating Cycle Length is chosen in requirements such as the minimum angle of diffraction of grating, manufacturing accuracy, and according to the normalization coordinate figure x of corresponding positions phase catastrophe point _kCalculate the coordinate figure of the phase jump point in each cycle of actual bit phase-plate;

4. utilize the electron-beam direct writing legal system to make mother matrix;

5. by the contact photolithography method, master pattern is transferred on the optical glass that scribbles photoresist and chromium film;

6. utilize wet etching technique, pattern etch to the chromium layer, is etched on the optical glass at last.

Technique effect of the present utility model is:

The utility model is eliminated the isocandela beam-splitting optical grating of zero level, no matter the position be 0 mutually, π two-value or when many-valued, can realize that all the even number lattice array beam splitting that the center senior spectrum point intensity of symmetry equates exports, and the homogeneity of diffraction spectra is not subjected to the influence of phase error.

Description of drawings

The synoptic diagram of Fig. 1 the utility model embodiment 1 structure.

The synoptic diagram of Fig. 2 the utility model embodiment 2 structures.

The beam splitting experimental demonstration device synoptic diagram of Fig. 3 zero suppression level Darman raster.

Fig. 4 is the synoptic diagram of the utility model 1 * 8 zero suppression level Darman raster far field construction.

Embodiment

The utility model is described in further detail below in conjunction with drawings and Examples.

Consult Fig. 1 earlier, the synoptic diagram of Fig. 1 the utility model embodiment 1 structure, it is the monocyclic normalized phase structure of two-value position phase zero suppression level Darman raster, it is with mid point (x=0.5, with dashed lines is indicated among the figure) be axis of symmetry, later half cycle phase jump point and preceding semiperiod phase jump point mirror image symmetry, the phasic difference of phase jump point is π.

11 phase jump points (comprising zero point and terminal point) are arranged, position phase 0, the two-value position phase Darman raster structure that π is alternate shown in the figure in the one-period.The border of every phase in the preceding semiperiod, the normalization coordinate x of promptly every phase catastrophe point ₁, x ₂, x ₃, x ₄Expression, the normalization coordinate of phase jump point is 1-x in the later half cycle ₄, 1-x ₃, 1-x ₂, 1-x ₁, the position phase 0 between every phase catastrophe point, π distributes alternately.The most frequently used and what be easy to process is this two-value phase board.

Fig. 2 is the synoptic diagram of the utility model embodiment 2 structures.This embodiment 2 is one many-valued phase zero suppression level Darman raster, seven phase jump points is arranged, the synoptic diagram of the Darman raster structure of six position phases in the unit period.The border of every phase is that normalization phase jump point coordinate is 0 in the preceding semiperiod, x ₁, x ₂, 0.5, everybody is worth mutually and uses θ ₁, θ ₂, θ ₃Expression, the phase jump point is 0.5 in the later half cycle, 1-x ₂, 1-x ₁, 1, corresponding position is respectively π+θ mutually ₃, π+θ ₂, π+θ ₁. the dotted line among the figure is represented central symmetry axis.This is a kind of in order to obtain higher diffraction efficiency, the position between every phase catastrophe point mutually also can be between [0,2 π] value, be called many-valued position phase zero suppression level Darman raster.The number of phase jump point can artificially be set in optimizing solution procedure according to actual needs in each cycle.

The characterising parameter of zero suppression level Darman raster has:

The splitting ratio 2N of 1, zero suppression level Darman raster: the coherent light of collimation is 2N by the number of the isocandela diffraction pattern that this zero suppression level Darman raster is produced.

2, for zero suppression level Darman raster, diffraction efficiency is defined as:

$\mathrm{\η}=2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{I}_i---\left(1\right)$

Wherein: N is the number of the equal order of diffraction of light intensity, I _iBe the light intensity peak of even light intensity order of diffraction i level, because the intensity of incident optical energy has been normalized to 1, so the following formula diffraction efficiency is defined as the ratio that each even order of diffraction time interior luminous energy summation accounts for incident optical energy.Should calculate the inferior light intensity of the positive and negative order of diffraction when calculating diffraction efficiency respectively, but because zero suppression level Darman raster has adopted the special construction of phase jump point about the perpendicular bisector mirror image symmetry of the mid point in each cycle, make the positive and negative order of diffraction time light intensity equate, so the negative order of diffraction light intensity of available positive order of diffraction light intensity representative.

3, characteristic dimension

Δ＝min|x _k+1-x _k| (2)

Wherein: x _kBe the phase jump point coordinate in the semiperiod, k is its subscript.

4, uniformity coefficient

$\mathrm{uni}=\frac{I_{\max }-I_{\min }}{I_{\max }+I_{\min }}---\left(3\right)$

In the formula: I _MaxAnd I _MinMaximal value and the minimum value of representing the required order of diffraction time middle light intensity respectively.By the conclusion of diffraction optics as can be known, given zero suppression level phase board, its far field construction light field distribution of amplitudes is:

$\left\{\begin{array}{c}A\left(0\right)=0\\ A\left(n\right)=\left(\frac{1}{\mathrm{n\π}}\right)\×(\underset{k=1}{\overset{K}{\mathrm{\Σ}}}-(\cos \left({\mathrm{\α}}_k\right)-\cos \left({\mathrm{\α}}_{k-1}\right)\left)\sin \right({\mathrm{\θ}}_k)+i\underset{k=1}{\overset{K}{\mathrm{\Σ}}}(\cos \left({\mathrm{\α}}_k\right)-\cos \left({\mathrm{\α}}_{k-1}\right)\left)\cos \right({\mathrm{\θ}}_k\left)\right)\end{array}\right.---\left(4\right)$

If fetch bit is two-value mutually: 0, π, then far field construction field amplitude can be written as:

$\left\{\begin{array}{c}A\left(0\right)=0\\ A\left(n\right)=\left(\frac{1}{\mathrm{n\π}}\right)\×\left(\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\right(-1{)}^k\left(\cos \right({\mathrm{\α}}_k)-\cos ({\mathrm{\α}}_{k-1}\left)\right)\end{array}\right.---\left(5\right)$

(4) and in (5) formula: α _k=2 π nx _k, n is that the order of diffraction is inferior, K is the number of SPA sudden phase anomalies point, x _kBe k phase jump point, θ _kBe k-1 to k position between mutually value mutually, light distribution is I (n)=A (n) A ^*(n).

In the manufacturing process of actual two-value position phase zero suppression level Darman raster, if cause the position to become θ mutually because of the error of etching depth, then its Zero-order diffractive light intensity and other diffraction intensities at different levels become:

$I\left(0\right)={\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="S2007201986526E00021.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\frac{\mathrm{\&theta;}}{2}---\left(6\right)$

$I\left(n\right)=\left(\frac{1}{\mathrm{\&pi;n}}{)}^2{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="S2007201986526E00021.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\frac{\mathrm{\&theta;}}{2}\right\{1+{(-1)}^{K+n}+2\underset{k=1}{\overset{K-1}{\mathrm{\&Sigma;}}}(-1{)}^k\cos ({2\mathrm{\&pi;nx}}_k\left)\right\}---\left(7\right)$

Formula (6) has been described the relation between position phase θ and the zero level light intensity I (0), for zero suppression level Darman raster, in the actual fabrication process, can pass through different etching depths, and promptly different positions is controlled the light intensity at zero point mutually.When the position was π mutually, the zero level spectrum disappeared formula (7) and formula (5) equivalence; When θ satisfies:

$\mathrm{\&theta;}=\mathrm{\&pi;}\&PlusMinus;2\mathrm{<figure-callout\; id="1"\; label="arctan"\; filenames="S2007201986526E00021.png"\; state="\{\{state\}\}">arctan</figure-callout>}\frac{1}{\mathrm{n\&pi;}}\sqrt{1+(-1{)}^{K+n}+2\underset{k=1}{\overset{K-1}{\mathrm{\&Sigma;}}}(-1{)}^k\cos \left(2\mathrm{\&pi;n}{x}_k\right)}---\left(8\right)$

The time, I (0)=I (n) can realize 1 * 3,1 * 5, the matrix lamp of 1 * 7 grade.For example, it to splitting ratio 1 * 6 zero suppression level Darman raster, when θ=(1 ± 0.20159) π, Zero-order diffractive light intensity and ± 1, ± 2, ± 3 order diffraction levels time light intensity equates that promptly 1 * 6 zero suppression level Darman raster has been realized 1 * 7 matrix lamp when phase place is (1 ± 0.20159) π, the diffraction efficiency of this moment is 0.6787, and uniformity coefficient is 8.9 * 10 ^-5

Formula (7) has been described the inferior light intensity of other each order of diffraction except that zero level, and from this formula as can be known, the light intensity ratio of n order diffraction light light intensity and n+1 level and θ are irrelevant.When the etching depth variation, when promptly θ changed, though the inferior light intensity of other each order of diffraction beyond the zero level changes, the ratio between them was constant, and the phase of ascending the throne error only influences diffraction efficiency, does not change uniformity coefficient.When the value of every phase catastrophe point was set by the optimization result, each the senior order of diffraction in the splitting ratio is inferior to be equated, i.e. I (n)/I (n+1)=1.Know that thus in the actual fabrication process, the light intensity of the senior diffraction spectra that each equates produces identical variation to different etching depths.

The utility model has provided each two-value of splitting ratio from 1 * 4 to 1 * 14 and the parameters optimization of the many-valued position Darman raster of zero suppression level mutually embodiment.The optimization index that adopts in the calculating is that uniformity coefficient is less than 10 ^-4, characteristic dimension is greater than 0.0002.Adopt formula (5) and quick descent algorithm to search out the two-value position Darman raster of zero suppression level mutually of splitting ratio from 1 * 4 to 1 * 14, it is as shown in table 1 that it optimizes numerical result.In order to obtain higher diffraction efficiency, our application of formula (4) has searched out the mutually value the best normalization coordinate figure of catastrophe point of phase board of many-valued position phase zero suppression level Darman raster of splitting ratio from 1 * 4 to 1 * 14 and the adjacent abrupt point, and the result is as shown in table 2.Table 1 and table 2 are less than 10 from uniformity coefficient ^-4, characteristic dimension is greater than the design parameter of the grating embodiment of the diffraction efficiency maximum of choosing at least 50 design parameters of 0.0002.It should be noted that, in order to save the space, the normalization phase jump point of only having listed the preceding semiperiod in table 1 and the table 2 and position are mutually, the inverted order of the normalization phase jump point in later half cycle by preceding each catastrophe point of semiperiod arranged to get and negatively added one and obtain, for many-valued position phase Darman raster, position mutually part is the result of preceding semiperiod actual bit after divided by π, and the position in later half cycle is that the contrary with the preceding semiperiod adds π to ordering and obtains mutually.

The beam splitting experimental demonstration device synoptic diagram of zero suppression level Darman raster of the present utility model as shown in Figure 3, monochromatic plane wave 1 impinges perpendicularly on zero suppression level Darman raster 2, on the focal plane 4 of fourier transform lens 3, produce the Fraunhofer diffraction pattern sample of Darman raster 2, promptly do not have the hot spot that the multi-level diffraction light intensity of zero level equates (only marked among the figure ± 1 and ± 2 grades) at lens.

Fig. 4 has shown that the utility model 1 * 8 eliminates the synoptic diagram of far field construction on the focal plane that the isocandela beam-splitting optical grating splitting ratio of Zero-order diffractive spectrum point is 8 lens.

The utility model adopts the center symmetry, π phase reversal structure, automatically eliminated the center zero order spectrum, therefore, the utility model both can on the thronely be to realize 1 * 2,1 * 4 of no center zero level spectrum point under the situation of π mutually, 1 * 6 ... the result, also can be on the throne mutually for realizing the matrix lamp of 1 * 3,1 * 5,1 * 7 grades under the situation of some particular value.Because matrix lamp is a basic optical function, has been widely used, and therefore, the utlity model has important application prospects.

Table 1 the utility model is eliminated the parameter of the isocandela beam-splitting optical grating two-value position phase embodiment of Zero-order diffractive spectrum point

Splitting ratio	Diffraction efficiency	Uniformity coefficient	Characteristic dimension	Preceding semiperiod phase jump point normalization coordinate figure
					1×4	0.6175	5.7×10 -5	0.01137	0、0.01137、0.14466、0.5
1×6	0.6442	8.9×10- 5	0.06108	0、0.15007、0.43892、0.5
					1×8	0.6669	1.3×10 -4	0.00083	0、0.00083、0.10894、0.14029、0.35088、 0.5
1×10	0.8211	7.7×10 -5	0.00113	0、0.12087、0.12234、0.13059、0.22680、 0.28328、0.28441、0.5
					1×12	0.6834	3.2×10 -4	0.00027	0、0.01441、0.06480、0.19650、0.22504、 0.35769、0.49973、0.5
1×14	0.6585	2.8×10 -4	0.00080	0、0.02212、0.07996、0.08076、0.13949、 0.15700、0.26995、0.36406、0.46288、0.5

Table 2 the utility model is eliminated the parameter of the many-valued position of the isocandela beam-splitting optical grating phase zero suppression level Darman raster embodiment of Zero-order diffractive spectrum point

Splitting ratio	Diffraction efficiency	Uniformity coefficient	Characteristic dimension	Preceding semiperiod phase jump point normalization coordinate figure	The position is worth mutually between the adjacent abrupt point
						1×4	0.8469	1.7×10 -5	0.04944	0、0.22672、0.27616、0.5	0.53084、 0.26092、0
1×6	0.8277	5.4×10 -5	0.15112	0、0.15800、0.30912、0.5	0、 0.27809、 1.56391
						1×8	0.8414	3.8×10 -5	0.07396	0、0.07396、0.20814、 0.35513、0.5	0、 0.21289、 1.79358、 0.76798
1×10	0.8586	1.1×10 -4	0.10609	0、0.10609、0.23197、 0.36863、0.5	0.74254、 0、 0.52544、 1.03374
						1×12	0.8482	3.2×10 -4	0.02474	0、0.13821、0.23273、 0.31761、0.34235、0.40176、 0.5	0.36676、 0.96830、 0、 0.23384、 0.44489、 1.94301
1×14	0.8108	2.2×10 -4	0.01079	0、0.09423、0.15202、 0.22664、0.23743、0.33904、 0.38853、0.46168、0.48838、 0.5	0.89947、 0.18923、 0.90715、 0.44655、 0、 0.02816、 0.57896、 0.72721、 0.36744

Claims (3)

1, a kind of isocandela beam-splitting optical grating of eliminating Zero-order diffractive spectrum point, the structure that it is characterized in that this grating is the zero suppression level Darman raster that the periodicity of a microstructure repeats, in each cycle of grating, phase jump point is about the perpendicular bisector mirror image symmetry in this cycle, position between the two-phase ortho position phase catastrophe point in later half cycle is worth mutually with respect to the position phase value drift π between the phase jump point of preceding semiperiod correspondence, each senior diffraction light light intensity is equal, i.e. I _{± 1}=I _{± 2}=...=I _±, wherein N is the positive integer greater than 1, and the splitting ratio of this grating is 2N, and the parameter of this grating adopts quick descent algorithm and appliance computer program optimization to calculate: the number K of SPA sudden phase anomalies point, k-1 are worth θ to k position between mutually mutually _k, and k phase jump point normalization coordinate figure x _k, wherein k be 1,2 ..., K.

2, the isocandela beam-splitting optical grating of elimination zero level according to claim 1, it is characterized in that the position between the described phase jump point is many-valued mutually, the parameter of described grating adopts quick descent algorithm to calculate by following formula and appliance computer program optimization:

$\left\{\begin{array}{c}A\left(0\right)=0\\ A\left(0\right)=\left(\frac{1}{\mathrm{n\&pi;}}\right)\&times;(\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}-(\cos \left({\mathrm{\&alpha;}}_k\right)-\cos \left({\mathrm{\&alpha;}}_{k-1}\right)\left)\sin \right({\mathrm{\&theta;}}_k)+i\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}(\cos \left({\mathrm{\&alpha;}}_k\right)-\cos \left({\mathrm{\&alpha;}}_{k-1}\right)\left)\cos \right({\mathrm{\&theta;}}_k\left)\right)\end{array}\right.$

In the formula: in the formula: α _k=2 π nx _k, n is that the order of diffraction is inferior, K is the number of SPA sudden phase anomalies point, x _kBe k phase jump point, θ _kBe k-1 to k position between mutually value mutually, light distribution is I (n)=A (n) A ^*(n).

3, the isocandela beam-splitting optical grating of elimination zero level according to claim 1, it is characterized in that the position between the described phase jump point is 0 mutually, π is alternate, and the parameter of described grating adopts quick descent algorithm to calculate by following formula and appliance computer program optimization:

$\left\{\begin{array}{c}A\left(0\right)=0\\ A\left(n\right)=\left(\frac{1}{\mathrm{n\&pi;}}\right)\&times;\left(\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\right(-1{)}^k\left(\cos \right({\mathrm{\&alpha;}}_k)-\cos ({\mathrm{\&alpha;}}_{k-1}\left)\right)\end{array}\right.$

In the formula: α _k=2 π nx _k, n is that the order of diffraction is inferior, K is the number of SPA sudden phase anomalies point, x _kBe k phase jump point, θ _kBe k-1 to k position between mutually value mutually, light distribution is I (n)=A (n) A ^*(n).

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