CN202305866U - Composite phase plates for expanding field depth of optical imaging system - Google Patents

Abstract

The utility model relates to the composite phase plates that three kinds are used for expanding field depth of optical imaging system, when the phase distribution function of one of phase-plate is formed by power function three times, logarithmic function A, exponential function and high math power function superposition, a dimensional expression of phase distribution function are as follows:

--- -- logarithmic function A

In formula: 1~α of α 7 is the parameter of the phase distribution function of the phase-plate; X is normalization aperture coordinate, and value range is [- 1,1]; Sgn is sign function, its value is -1 when as x ＞ 0, its value is 1, x ＜ 0. The utility model provides three kinds of composite phase plates for expanding field depth of optical imaging system that system can be made more insensitive to defocus and sharp keen clearly big depth image can be obtained.

Description

Be used to expand the combined type phase-plate of the optical imaging system depth of field

Technical field

The utility model belongs to optical field, relates to a kind of phase mask plate, relates in particular to a kind of combined type phase-plate that is used to expand the optical imaging system depth of field.

Background technology

The depth of field of expanding optical imaging system always is the focus of academia's research.Since 20th century the mid-80; Though being suggested, panoramic method is used to expand the depth of field; But doctor Dowski and Cathey up to Univ Colorado-Boulder USA teach after the wavefront coded notion of nineteen ninety-five proposition, and depth of field continuation has just had breakthrough truly.

Through on aperture plane, entrance pupil face or the emergent pupil face of traditional imaging system, adding the phase mask plate through particular design, system will and cause that the factor of out of focus is insensitive to out of focus so.With the one dimensional optical system is example, and its out of focus optical transfer function OTF (Optical transfer function) can obtain through the auto-correlation computation of generalized pupil function, and is as follows:

$H(u,W_{20})=\frac{1}{2}\&CenterDot;\underset{-(1-|u|/2)}{\overset{1-\left|u\right|/2}{\&Integral;}}\exp (j\&CenterDot;(2\mathrm{<figure-callout\; id="20"\; label="k\; W"\; filenames="HDA0000098485480000051.png"\; state="\{\{state\}\}">k</figure-callout>}{W}_{}{}_{20}\mathrm{ux}+f(x+u/2)-f(x-u/2)))\mathrm{dx}$

Wherein, u and x are respectively normalized spatial frequency and aperture plane lateral coordinates; W ₂₀It is maximum defocus wave aberration coefficient; K is a wave number; F represents the universal expression formula of employed phase mask plate.

For traditional imaging system, the f item in the following formula does not exist, and the formula that embodies that therefore can obtain out of focus OTF is:

$H(u,W_{20})=\frac{\sin (2\mathrm{<figure-callout\; id="20"\; label="k\; W"\; filenames="HDA0000098485480000051.png"\; state="\{\{state\}\}">k</figure-callout>}{W}_{}{}_{20}\&CenterDot;(1-\frac{\left|u\right|}{2}))}{2k{W}_{20}u}u\&NotEqual;0$

Can see that when system did not introduce phase-plate, its OTF was highstrung to out of focus, and zero point can periodically occur, thereby cause irreversible information loss in the frequency space.But in case with the cube phase-plate (f (x)=α x of doctor E.R.Dowski institute utility model ³) be incorporated on the entrance pupil face of optical system after, we just can obtain a diverse out of focus OTF through the static phase method of approximation, as follows:

$H(u,W_{20})\&ap;\frac{1}{2}\&CenterDot;\sqrt{\frac{\mathrm{\&pi;}}{\left|3\mathrm{\&alpha;u}\right|}}\&CenterDot;\exp (j\&CenterDot;(\frac{\mathrm{\&alpha;}{u}^3}{4}-\frac{k^{2}u{W^2}_{20}}{3\mathrm{\&alpha;}})+j\&CenterDot;\mathrm{sgn}\left(u\right)\&CenterDot;\frac{\mathrm{\&pi;}}{4})$ u≠0

Obviously, this moment out of focus OTF mould, promptly MTF (Modulation transfer function) has nothing to do with out of focus wave aberration coefficient, that is to say that the cube phase-plate can make the MTF of system insensitive to out of focus; Though the phase bit position of OTF is relevant with out of focus parameter W20, as long as modulation factor α increases, its dependency degree to W20 will significantly reduce.Simultaneously of paramount importancely be; After having added phase-plate; MTF is just having decline to a certain degree within the effective frequency range on amplitude, and does not have zero point or nearly zero point, when promptly out of focus appears in system; The information that exceeds the primal system field depth is not lost, and just can be recovered effectively through the digital image restoration algorithm afterwards.Simultaneously because phase-plate can not impact logical light quantity and the resolution of system, so wavefront coded be a kind of novel depth of field expansion imaging technique that is different from very much reduced bore method, central obscuration method or apodization.

Though it is of a great variety to be used for the phase-plate of depth of field continuation, whether having the phase-plate with better performance still is the focus of research.If the consistance of the pairing out of focus MTF of phase-plate under different defocusing amounts is high more, and zero point or nearly zero point do not occur, so just can think that this phase-plate has strong depth of field expansion capability.

The utility model content

The utility model provides three kinds can make the combined type phase-plate that is used to expand the optical imaging system depth of field that system is more insensitive to out of focus and can obtain sharp keen big depth image clearly.

The technical solution of the utility model is: the utility model provides three kinds of combined type phase-plates that are used to expand the optical imaging system depth of field; Its special character is: when the PHASE DISTRIBUTION function of phase-plate was formed by stacking third power function, logarithmic function A, exponential function and high order power function, the one dimension expression formula of its PHASE DISTRIBUTION function was:

$f_1\left(x\right)=({\mathrm{\&alpha;}}_1\&CenterDot;x^3)$

$+\{{\mathrm{\&alpha;}}_2\&CenterDot;\mathrm{Sgn}\left(x\right)\&CenterDot;x^2\&CenterDot;[\mathrm{Log}\left(\right|x\left|\right)+{\mathrm{\&alpha;}}_3\left]\right\}$ -----logarithmic function A

$+[{\mathrm{\&alpha;}}_4\&CenterDot;x\&CenterDot;\exp ({\mathrm{\&alpha;}}_5\&CenterDot;x^2)]$

$+[{\mathrm{\&alpha;}}_6\&CenterDot;\mathrm{sgn}\left(x\right)\&CenterDot;{\left|x\right|}^{{\mathrm{\&alpha;}}_7}]$

In the formula:

α 1～α 7 is PHASE DISTRIBUTION function parameters of said phase-plate;

X is a normalization aperture coordinate, and its span is [1,1];

Sgn is-symbol function, its value is 1 when x＞0, x＜0 o'clock its value is-1.

When the PHASE DISTRIBUTION function of phase-plate is when being formed by stacking third power function, logarithmic function A, exponential function, high order power function and logarithmic function B, the one dimension expression formula of its PHASE DISTRIBUTION function is:

$f_2\left(x\right)=({\mathrm{\&alpha;}}_1\&CenterDot;x^3)$

$+\{{\mathrm{\&alpha;}}_2\&CenterDot;\mathrm{Sgn}\left(x\right)\&CenterDot;x^2\&CenterDot;[\mathrm{Ln}\left(\right|x\left|\right)+{\mathrm{\&alpha;}}_3\left]\right\}$ -----logarithmic function A

$+[{\mathrm{\&alpha;}}_4\&CenterDot;x\&CenterDot;\exp ({\mathrm{\&alpha;}}_5\&CenterDot;x^2)]$

$+[{\mathrm{\&alpha;}}_6\&CenterDot;\mathrm{sgn}\left(x\right)\&CenterDot;{\left|x\right|}^{{\mathrm{\&alpha;}}_7}]$

$+\{{\mathrm{\&alpha;}}_8\&CenterDot;\mathrm{Sgn}\left(x\right)\&CenterDot;x^2\&CenterDot;[\mathrm{Ln}\left(\right|\left|x\right|+{\mathrm{\&alpha;}}_9\left|\right)\left]\right\}$ -----logarithmic function B

In the formula:

α 1～α 9 is PHASE DISTRIBUTION function parameters of said phase-plate;

X is a normalization aperture coordinate, and its span is [1,1];

Sgn is-symbol function, x＞0 o'clock its value is 1, x＜0 o'clock its value is for-1.

When the PHASE DISTRIBUTION function of phase-plate is when being formed by stacking third power function, logarithmic function A, exponential function, high order power function, logarithmic function B and sine function, the one dimension expression formula of its PHASE DISTRIBUTION function is:

$f_3\left(x\right)=({\mathrm{\&alpha;}}_1\&CenterDot;x^3)$

$+\{{\mathrm{\&alpha;}}_2\&CenterDot;\mathrm{Sgn}\left(x\right)\&CenterDot;x^2\&CenterDot;[\mathrm{Ln}\left(\right|x\left|\right)+{\mathrm{\&alpha;}}_3\left]\right\}$ -----logarithmic function A

$+[{\mathrm{\&alpha;}}_4\&CenterDot;x\&CenterDot;\exp ({\mathrm{\&alpha;}}_5\&CenterDot;x^2)]$

$+[{\mathrm{\&alpha;}}_6\&CenterDot;\mathrm{sgn}\left(x\right)\&CenterDot;{\left|x\right|}^{{\mathrm{\&alpha;}}_7}]$

$+\{{\mathrm{\&alpha;}}_8\&CenterDot;\mathrm{Sgn}\left(x\right)\&CenterDot;x^2\&CenterDot;[\mathrm{Ln}\left(\right|\left|x\right|+{\mathrm{\&alpha;}}_9\left|\right)\left]\right\}$ -----logarithmic function B

$+[{\mathrm{\&alpha;}}_{10}\&CenterDot;\sin ({\mathrm{\&alpha;}}_{11}\&CenterDot;x)]$

In the formula:

α 1～α 11 is PHASE DISTRIBUTION function parameters of said phase-plate;

X is a normalization aperture coordinate, and its span is [1,1];

Sgn is-symbol function, x＞0 o'clock its value is 1, x＜0 o'clock its value is for-1.

The utility model has the advantages that:

The novel combined phase mask plate that the utility model designed can reduce the susceptibility of system to out of focus more significantly; Great variation can not take place with the change of out of focus parameter in the modulation transfer function (MTF) that is whole optical system; And zero point or nearly zero point can not appear, so can not cause losing of image detail information in the passband scope.After middle blurred picture process deconvolution processing, just can obtain sharp keen big clearly depth image.

Description of drawings

Fig. 1 is the face type curve family of first phase-plate that provides of the utility model;

Fig. 2 is the face type curve family of second phase-plate that provides of the utility model;

Fig. 3 is the face type curve family of the third phase position plate that provides of the utility model;

Fig. 4 is to use the utility model proposed under the different Th conditions of Fisher information evaluation three kinds of combined type phase-plates and the other two kinds of existing combined type phase-plates synoptic diagram to the inhibition ability of out of focus;

Three kinds of combined type phase-plates that Fig. 5 is to use that the utility model proposed under the different Th conditions of Fisher information evaluation and six kinds of typical phase-plates are to the synoptic diagram of the inhibition ability of out of focus.

Embodiment

Tightly around the research focus, the mode through stack has proposed three kinds of novel combined phase mask plates that are used to expand the optical imaging system depth of field to the utility model.Analysis result shows that new phase-plate has better out of focus unchangeability, but before depth of field continuation ability new, old phase-plate is estimated, is the first step based on the face type optimization under the uniform principles.Because the decline meeting of the MTF that introducing caused of phase-plate produces adverse influence to follow-up image restoration, so the optimization of face type should serve as that constraint is carried out with minimum acceptable MTF (i.e. Th in table 1, table 2 and the table 3).

The phase-plate that is used to expand the optical imaging system depth of field that the utility model is related, its PHASE DISTRIBUTION function is formed by existing dissimilar phase mask plate mutual superposition.The combined type phase-plate should be near aperture plane, entrance pupil plane or the emergent pupil plane of imaging system when being provided with.Can also phase-plate face type be arranged on the lens surface near system aperture plane, entrance pupil face or emergent pupil face of imaging lens.

When above-mentioned phase-plate PHASE DISTRIBUTION function was formed by stacking third power function, logarithmic function A, exponential function and high order power function, its one dimension function expression was:

$f_1\left(x\right)=({\mathrm{\&alpha;}}_1\&CenterDot;x^3)$

$+\{{\mathrm{\&alpha;}}_2\&CenterDot;\mathrm{Sgn}\left(x\right)\&CenterDot;x^2\&CenterDot;[\mathrm{Log}\left(\right|x\left|\right)+{\mathrm{\&alpha;}}_3\left]\right\}$ -----logarithmic function A

$+[{\mathrm{\&alpha;}}_4\&CenterDot;x\&CenterDot;\exp ({\mathrm{\&alpha;}}_5\&CenterDot;x^2)]$

$+[{\mathrm{\&alpha;}}_6\&CenterDot;\mathrm{sgn}\left(x\right)\&CenterDot;{\left|x\right|}^{{\mathrm{\&alpha;}}_7}]$

In the formula, α 1～α 7 is said phase-plate PHASE DISTRIBUTION function parameters, and x is a normalization aperture coordinate, and its span is [1,1].Sgn is-symbol function, x＞0 o'clock its value is 1, x＜0 o'clock its value is for-1.

After use simulated annealing is carried out multi-parameters optimization to above-mentioned phase-plate, just can obtain the optimum face shape parameter under the pairing various boundary conditions of phase-plate, as shown in table 1; And as shown in Figure 1 with the pairing one dimension PHASE DISTRIBUTION of these parameters, wherein each bar curve (equals 0.21,0.25 with Th corresponding to the parameter shown in one group of table 1; 0.29 0.33 is example, Fig. 2 and 3 together); Horizontal ordinate is the aperture coordinate after the normalization, and ordinate is phase modulation (PM) intensity f ₁

Table 1

Th	α1	α2	α3	α4	α5	α6	α7
								0.21	63.04	86.06	0.47	71.86	1.06	55.25	1.27
0.23	56.56	62.07	0.27	61.75	1.19	99.82	2.01
								0.25	22.82	96.75	0.26	74.67	1.07	18.46	1.94
0.27	48.46	63.52	0.15	68.93	0.83	53.30	2.75
								0.29	50.57	57.95	0.007	14.52	2.24	48.60	1.65
0.31	49.53	54.50	0.12	5.46	2.76	70.45	2.56
								0.33	43.75	65.96	0.17	6.51	2.01	98.88	2.76
0.35	6.85	43.06	0.21	17.28	1.78	99.24	2.30

When above-mentioned phase-plate PHASE DISTRIBUTION function is when being formed by stacking third power function, logarithmic function A, exponential function, high order power function and logarithmic function B, its one dimension function expression is:

$f_2\left(x\right)=({\mathrm{\&alpha;}}_1\&CenterDot;x^3)$

$+\{{\mathrm{\&alpha;}}_2\&CenterDot;\mathrm{Sgn}\left(x\right)\&CenterDot;x^2\&CenterDot;[\mathrm{Ln}\left(\right|x\left|\right)+{\mathrm{\&alpha;}}_3\left]\right\}$ -----logarithmic function A

$+[{\mathrm{\&alpha;}}_4\&CenterDot;x\&CenterDot;\exp ({\mathrm{\&alpha;}}_5\&CenterDot;x^2)]$

$+[{\mathrm{\&alpha;}}_6\&CenterDot;\mathrm{sgn}\left(x\right)\&CenterDot;{\left|x\right|}^{{\mathrm{\&alpha;}}_7}]$

$+\{{\mathrm{\&alpha;}}_8\&CenterDot;\mathrm{Sgn}\left(x\right)\&CenterDot;x^2\&CenterDot;[\mathrm{Ln}\left(\right|\left|x\right|+{\mathrm{\&alpha;}}_9\left|\right)\left]\right\}$ -----logarithmic function B

In the formula, α 1～α 9 is said phase-plate PHASE DISTRIBUTION function parameters, and x is a normalization aperture coordinate, and its span is [1,1].Sgn is-symbol function, x＞0 o'clock its value is 1, x＜0 o'clock its value is for-1.

After use simulated annealing is carried out multi-parameters optimization to above-mentioned phase-plate; Just can obtain the optimum face shape parameter under the pairing various boundary conditions of phase-plate; As shown in table 2, and as shown in Figure 2 with the pairing one dimension PHASE DISTRIBUTION of these parameters, wherein each bar curve is corresponding to the parameter shown in one group of table 2; Horizontal ordinate is the aperture coordinate after the normalization, and ordinate is phase modulation (PM) intensity f ₂

Table 2

Th	α1	α2	α3	α4	α5	α6	α7	α8	α9
										0.21	57.36	86.15	0.41	93.29	0.98	85.25	2.03	36.96	0.29
0.23	57.61	56.70	0.17	67.20	1.18	76.36	1.33	20.24	1.64
										0.25	4.96	65.27	0.21	91.64	1.09	2.34	1.01	66.50	1.34
0.27	9.23	63.85	0.33	38.33	1.58	56.69	1.29	72.14	0.31
										0.29	61.38	93.08	0.05	7.15	1.78	93.50	2.47	0.58	0.72
0.31	57.23	71.44	0.39	12.83	0.10	91.93	2.68	51.19	1.46
										0.33	31.65	69.07	0.29	23.97	0.81	97.87	2.70	52.37	0.63
0.35	40.64	69.28	0.05	6.68	2.04	86.77	2.69	43.11	0.68

When above-mentioned phase-plate PHASE DISTRIBUTION function is when being formed by stacking third power function, logarithmic function A, exponential function, high order power function, logarithmic function B and sine function, its one dimension function expression is:

$f_3\left(x\right)=({\mathrm{\&alpha;}}_1\&CenterDot;x^3)$

$+\{{\mathrm{\&alpha;}}_2\&CenterDot;\mathrm{Sgn}\left(x\right)\&CenterDot;x^2\&CenterDot;[\mathrm{Ln}\left(\right|x\left|\right)+{\mathrm{\&alpha;}}_3\left]\right\}$ -----logarithmic function A

$+[{\mathrm{\&alpha;}}_4\&CenterDot;x\&CenterDot;\exp ({\mathrm{\&alpha;}}_5\&CenterDot;x^2)]$

$+[{\mathrm{\&alpha;}}_6\&CenterDot;\mathrm{sgn}\left(x\right)\&CenterDot;{\left|x\right|}^{{\mathrm{\&alpha;}}_7}]$

$+\{{\mathrm{\&alpha;}}_8\&CenterDot;\mathrm{Sgn}\left(x\right)\&CenterDot;x^2\&CenterDot;[\mathrm{Ln}\left(\right|\left|x\right|+{\mathrm{\&alpha;}}_9\left|\right)\left]\right\}$ -----logarithmic function B

$+[{\mathrm{\&alpha;}}_{10}\&CenterDot;\sin ({\mathrm{\&alpha;}}_{11}\&CenterDot;x)]$

In the formula, α 1～α 11 is said phase-plate PHASE DISTRIBUTION function parameters, and x is a normalization aperture coordinate, and its span is [1,1].Sgn is-symbol function, x＞0 o'clock its value is 1, x＜0 o'clock its value is for-1.

After use simulated annealing is carried out multi-parameters optimization to above-mentioned phase-plate; Just can obtain the optimum face shape parameter under the pairing various boundary conditions of phase-plate; As shown in table 3, and as shown in Figure 3 with the pairing one dimension PHASE DISTRIBUTION of these parameters, wherein each bar curve is corresponding to the parameter shown in one group of table 3; Horizontal ordinate is the aperture coordinate after the normalization, and ordinate is phase modulation (PM) intensity f ₃

Table 3

Th	α1	α2	α3	α4	α5	α6	α7	α8	α9	α10	α11
												0.21	43.33	91.83	0.55	69.74	1.16	26.11	1.39	69.76	1.98	35.58	0.08
0.23	58.42	62.17	0.12	78.15	1.09	79.76	1.34	39.94	0.54	33.11	1.08

0.25	1.03	51.07	0.15	89.70	1.16	37.23	1.91	9.82	1.87	59.51	1.38
												0.27	50.30	62.09	0.24	19.80	1.79	92.63	2.06	91.63	0.15	63.93	1.32
0.29	47.28	36.86	0.10	37.53	1.05	57.46	2.34	88.81	1.00	39.05	1.89
												0.31	49.10	65.50	0.03	13.94	1.83	42.59	2.04	32.63	1.45	39.84	0.56
0.33	15.18	71.98	0.16	11.64	2.34	25.93	2.03	89.66	0.90	3.40	0.93
												0.35	12.27	61.20	0.05	30.80	1.27	57.80	1.47	70.87	1.80	31.00	0.33

In above-mentioned table 1, table 2 and the table 3, symbol Th is a threshold value, and satisfies ∫ MTF (u, W ₂₀=0, P) du>=Th, wherein MTF is the modulation transfer function of wavefront coded system; U, W ₂₀And P is respectively the normalization spatial frequency, out of focus wave aberration coefficient and phase-plate parameter.Th is used for the degree that constrained system MTF reduces at phase-plate face type optimizing process, and promptly the Th value is big more, and the pairing MTF curve of system after optimizing is just high more, otherwise low more.

Curve contrast by Fig. 1, Fig. 2 and Fig. 3 can see that there is some difference between the pairing optimum face type curve of combined type phase-plate, similar inequality, and this has just determined its out of focus to suppress the size of ability.

Fisher information representation system is to the susceptibility of out of focus, and its value is more little, and system is just insensitive more to out of focus so.According to the definition of Fisher information, when out of focus parameter span was 0-9 π, the pairing Fisher information of which kind of phase-plate curve was low more, and so this phase-plate is good more to the insensitivity of out of focus, that is to say that it has stronger depth of field expansion capability.

Like Fig. 4 and shown in Figure 5; Three kinds of combined type phase-plates that the utility model proposed carry out after the multiparameter combined optimization; Its insensitivity to out of focus has had raising clearly, especially when the modulation transfer function MTF that requires wavefront coded system when higher, when promptly the Th value is big; The raising of this performance is especially obvious because new combined type phase-plate corresponding Fisher curve in the position of big defocusing amount tangible reduction is arranged.

In Fig. 4, the pairing Fisher information of three kinds of novel combined phase-plates that the utility model proposed is all littler than the Fisher information of existing two kinds of combined type phase-plates, shows that promptly it has stronger out of focus and suppresses ability; Six width of cloth images of Fig. 4 correspond respectively to Th and equal 0.23; 0.25,0.27,0.29; 0.31 and 0.33, and the out of focus scope is 0～9 π.Black, powder, blue or green corresponding to new combined type phase-plate f ₁, f ₂And f ₃, red and indigo plant is then corresponding to other two kinds of existing combined type phase-plates, and the phase-plate that wherein red expression is formed by stacking cube function and logarithmic function A is blue then represent the phase-plate that is formed by stacking cube function, logarithmic function A and exponential function.Wherein, horizontal ordinate is the out of focus parameter, and ordinate is a Fisher information.

Fig. 5 has then provided the performance comparison between novel combined phase-plate and the six kinds of single phase-plates, and six width of cloth images correspond respectively to Th and equal 0.21,0.23, and 0.25,0.27,0.31 and 0.33, and the out of focus scope is 0～9 π.Wherein not the curve of zone circle corresponding to new combined type phase-plate f ₁, f ₂, f ₃, and above-mentioned two kinds of existing combined type phase-plates; The curve of zone circle is then represented single phase-plate: cube type, logarithm A type, logarithm Type B, exponential type, high order square and sinusoidal pattern.Wherein, horizontal ordinate is the out of focus parameter, and ordinate is a Fisher information.

Can see that the novel phase-plate that the utility model proposed can make system more insensitive to out of focus, when especially the Th value is bigger, more remarkable to the inhibition effect of out of focus.In addition, three kinds of novel combined phase-plates are when the Th value is bigger, and its inhibition ability to out of focus almost can't be distinguished, because its pairing Fisher information curve coincides together basically.

With employed phase-plate in the prior art comparatively speaking; Use the related novel combined phase-plate of the utility model can make wavefront coded system that out of focus is become more insensitive; Great variation can not take place with the change of out of focus parameter in the modulation transfer function (MTF) that is whole imaging system; And zero point or nearly zero point can not appear, so can not cause losing of image detail information in the passband scope.After middle blurred picture process deconvolution processing, we just can obtain sharp keen depth image clearly.Because the MTF of system has fabulous stability, only use a digital filter just can the middle blurred picture of all positions to be restored simultaneously.

The related follow-on phase-plate of the utility model is used for wavefront coded imaging technique, preferably is arranged near the aperture of imaging system, near the entrance pupil or near the emergent pupil.If because imaging system has certain restriction to its operating distance, volume, quality or number of elements etc.; So also can be directly the face type of phase-plate be processed on certain surface of existing imaging lens; But in order to bring into play the performance of phase-plate to greatest extent, this surface is preferably near system aperture plane, entrance pupil face or emergent pupil face.

Claims (3)

1. combined type phase-plate that is used to expand the optical imaging system depth of field, it is characterized in that: the PHASE DISTRIBUTION function of said combined type phase-plate is formed by stacking third power function, logarithmic function A, exponential function and high order power function; The one dimension expression formula of the PHASE DISTRIBUTION function of said combined type phase-plate is:

$f_1\left(x\right)=({\mathrm{\&alpha;}}_1\&CenterDot;x^3)$

$+\{{\mathrm{\&alpha;}}_3\&CenterDot;\mathrm{Sgn}\left(x\right)\&CenterDot;x^2\&CenterDot;[\mathrm{Log}\left(\right|x\left|\right)+{\mathrm{\&alpha;}}_3\left]\right\}$ -----logarithmic function A

$+[{\mathrm{\&alpha;}}_4\&CenterDot;x\&CenterDot;\exp ({\mathrm{\&alpha;}}_5\&CenterDot;x^2)]$

$+[{\mathrm{\&alpha;}}_6\&CenterDot;\mathrm{sgn}\left(x\right)\&CenterDot;{\left|x\right|}^{{\mathrm{\&alpha;}}_7}]$

In the formula:

α 1～α 7 is PHASE DISTRIBUTION function parameters of said phase-plate;

X is a normalization aperture coordinate, and its span is [1,1];

Sgn is-symbol function, its value is 1 when x＞0, x＜0 o'clock its value is-1.

2. combined type phase-plate that is used to expand the optical imaging system depth of field, it is characterized in that: the PHASE DISTRIBUTION function of said combined type phase-plate is to be formed by stacking third power function, logarithmic function A, exponential function, high order power function and logarithmic function B; The one dimension expression formula of the PHASE DISTRIBUTION function of said combined type phase-plate is:

$f_2\left(x\right)=({\mathrm{\&alpha;}}_1\&CenterDot;x^3)$

$+\{{\mathrm{\&alpha;}}_2\&CenterDot;\mathrm{Sgn}\left(x\right)\&CenterDot;x^2\&CenterDot;[\mathrm{Ln}\left(\right|x\left|\right)+{\mathrm{\&alpha;}}_3\left]\right\}$ -----logarithmic function A

$+[{\mathrm{\&alpha;}}_4\&CenterDot;x\&CenterDot;\exp ({\mathrm{\&alpha;}}_5\&CenterDot;x^2)]$

$+[{\mathrm{\&alpha;}}_6\&CenterDot;\mathrm{sgn}\left(x\right)\&CenterDot;{\left|x\right|}^{{\mathrm{\&alpha;}}_7}]$

$+\{{\mathrm{\&alpha;}}_8\&CenterDot;\mathrm{Sgn}\left(x\right)\&CenterDot;x^2\&CenterDot;[\mathrm{Ln}\left(\right|\left|x\right|+{\mathrm{\&alpha;}}_9\left|\right)\left]\right\}$ -----logarithmic function B

In the formula:

α 1～α 9 is PHASE DISTRIBUTION function parameters of said phase-plate;

X is a normalization aperture coordinate, and its span is [1,1];

Sgn is-symbol function, x＞0 o'clock its value is 1, x＜0 o'clock its value is for-1.

3. combined type phase-plate that is used to expand the optical imaging system depth of field, it is characterized in that: the PHASE DISTRIBUTION function of said combined type phase-plate is to be formed by stacking third power function, logarithmic function A, exponential function, high order power function, logarithmic function B and sine function; The one dimension expression formula of the PHASE DISTRIBUTION function of said combined type phase-plate is:

$f_3\left(x\right)=({\mathrm{\&alpha;}}_1\&CenterDot;x^3)$

$+\{{\mathrm{\&alpha;}}_2\&CenterDot;\mathrm{Sgn}\left(x\right)\&CenterDot;x^2\&CenterDot;[\mathrm{Ln}\left(\right|x\left|\right)+{\mathrm{\&alpha;}}_3\left]\right\}$ -----logarithmic function A

$+[{\mathrm{\&alpha;}}_4\&CenterDot;x\&CenterDot;\exp ({\mathrm{\&alpha;}}_5\&CenterDot;x^2)]$

$+[{\mathrm{\&alpha;}}_6\&CenterDot;\mathrm{sgn}\left(x\right)\&CenterDot;{\left|x\right|}^{{\mathrm{\&alpha;}}_7}]$

$+\{{\mathrm{\&alpha;}}_8\&CenterDot;\mathrm{Sgn}\left(x\right)\&CenterDot;x^2\&CenterDot;[\mathrm{Ln}\left(\right|\left|x\right|+{\mathrm{\&alpha;}}_9\left|\right)\left]\right\}$ -----logarithmic function B

$+[{\mathrm{\&alpha;}}_{10}\&CenterDot;\sin ({\mathrm{\&alpha;}}_{11}\&CenterDot;x)]$

In the formula:

α 1～α 11 is PHASE DISTRIBUTION function parameters of said phase-plate;

X is a normalization aperture coordinate, and its span is [1,1];

Sgn is-symbol function, x＞0 o'clock its value is 1, x＜0 o'clock its value is for-1.

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