Multi-order diffraction lens manufacturing error analysis method based on ring band reconstruction differential

Abstract

The invention belongs to the field of multi-order diffraction lens processing, and particularly relates to a multi-order diffraction lens manufacturing error analysis method based on ring band reconstruction differential. The method comprises the following steps: firstly, constructing an error function epsilon for a morphology error type caused by processing of MDL; based on the constructed error function epsilon, an MDL error height distribution matrix hij is obtained; then calculating a diffraction light field of the MDL at a focal plane position; and finally, calculating optical performance indexes of the MDL under the influence of the error, wherein the optical performance indexes comprise relative focus position deviation and relative focusing efficiency loss. According to the method, optical performance related analysis can be effectively carried out on complex morphology errors formed in the MDL manufacturing process; the change trend and interval of the optical performance loss of the MDL under the influence of manufacturing errors can be accurately analyzed through theoretical calculation and analogue simulation; the method has high applicability and accuracy for optical performance analysis work of the MDL under any error morphology; the process is convenient to improve, and the practicability is high.

Description

Technical Field

[0001] The invention belongs to the field of multi-order diffraction lens processing, and in particular relates to a multi-order diffraction lens manufacturing error analysis method based on annular zone reconstruction differential. Background Art

[0002] The design and application of wide-band achromatic imaging devices have always been a research hotspot in the field of optical imaging. Traditional optical imaging systems generally use the following two solutions for achromatic imaging design: gluing multiple groups of positive and negative lenses made of different materials, and mixing refractive lenses with diffractive lenses. These two achromatic solutions are inseparable from traditional curvature lenses, which causes the volume of the optical imaging system to become redundant as the achromatic performance improves. The superposition of multiple lenses also increases the overall cost of system design.

[0003] Multi-order diffractive-lens (MDL) has the function of realizing broadband achromatism with a single lens. It consists of several groups of concentric rings with equal width. The optimal height distribution of each ring is found through optimization algorithm to provide target phase shift at different lens positions, so that MDL can realize achromatic focusing function of multiple incident wavelengths in the far-field target area.

[0004] Since the characteristic size of MDL is in the micron level, most of the current processing techniques will cause certain distortion on the ring surface, forming an error morphology. Relevant design research at home and abroad also shows that the actual performance of the processed MDL has a large deviation from the theoretical design value. Therefore, it is of practical significance to conduct relevant error analysis work to improve lens design and processing paths. Sourangsu Banerji et al. proposed an error analysis method for the ring height h and width w. By applying offsets Δh and Δw based on normal distribution to each ring height or width, the optical performance loss caused by the MDL ring height and width errors caused by the manufacturing process can be effectively solved. However, since the number of analysis objects of this error analysis method is still the original number of rings, this method cannot effectively fit, model and analyze the more common and complex MDL ring morphology errors. Summary of the invention

[0005] The present invention provides a method for analyzing manufacturing errors of a multi-order diffraction lens based on annular zone reconstruction differential, so as to solve the problem of poor applicability of the MDL manufacturing error analysis method in the prior art.

[0006] In order to achieve the above object, the technical solution of the present invention is implemented as follows: A method for analyzing manufacturing errors of multi-order diffraction lenses based on annular zone reconstruction differentials comprises the following steps:

[0007] Step 1: Construct an error function ε for the type of morphological error caused by processing in MDL;

[0008] Step 2: Based on the constructed error function ε, obtain the error height distribution h ij ;

[0009] Step 3, calculate the diffracted light field of the MDL at the focal plane under the influence of the error;

[0010] Step 4: Calculate the optical performance index of MDL under the influence of errors.

[0011] Furthermore, in the above step 2, the ideal step height distribution matrix h i Perform matrix transformation based on the error function ε to obtain the concave step height distribution matrix h ij :

[0012]

[0013] Furthermore, in the above step 1, a nonlinear regression model is used to construct the error function ε:

[0014]

[0015] In formula (2), e is the concavity factor, and the maximum concavity degree of a single ring is Δh = h i ×e,j is the index value of the number of micromolecular rings p, that is, p = 1, 2, 3, ..., j; the width of the sub-ring is w p =w / p.

[0016] Furthermore, in the above step 3, the light intensity distribution curve at the MDL focal plane containing error information is:

[0017] I(x',y',λ,f)=|U(x',y',λ,f) 2 (3).

[0018] Furthermore, in the above step 4, the optical performance index includes the average focal position and the average focusing efficiency The relative deviation rate.

[0019] Furthermore, in the above step 4, the average focal position It is defined as the average value of the coordinates corresponding to the maximum axial (z-axis) light intensity I(z):

[0020]

[0021] The relative deviation rate compared to the theoretical value is:

[0022]

[0023] Furthermore, in the above step 4, the average focusing efficiency It is defined as the average ratio of the optical power in the focal plane Airy disk area to the optical power within the MDL aperture:

[0024]

[0025] Where: n is the total number of working wavelengths;

[0026] The relative deviation rate compared to the theoretical value is:

[0027] Compared with the prior art, the advantages of the present invention are:

[0028] 1. The present invention seeks the annular ring morphology errors caused by different MDL manufacturing processes, constructs an error function, and realizes the construction of the MDL error model by mapping the error function to the ideal height distribution. Then, the commonly used calculation method can be selected to solve the diffraction light field distribution at the focus of the MDL, and then the optical performance loss of the MDL under the influence of the calculation error (including relative focus position offset, relative focusing efficiency loss) is performed to perform the MDL error analysis work of the corresponding manufacturing process / error type. Since the initial ring is subjected to differential analytical operations, any error morphology distribution can be effectively approximated by regulating the height distribution of the sub-rings. Therefore, the present invention can effectively perform optical performance-related analysis on the complex morphology errors formed in the MDL manufacturing process.

[0029] 2. Steps 1 and 2 of the present invention convert the abstract error morphology into a quantifiable sub-wavelength size structure by differential analysis of the error profile, and can accurately analyze the changing trend and range of the optical performance loss of MDL under the influence of manufacturing errors through theoretical calculation and simulation.

[0030] 3. Since the error function ε of step 2 can be characterized by fitting methods such as nonlinear regression, the specific function form depends on the annular error height distribution of a single annular zone (or the entire MDL) caused by various actual MDL processing technologies, and thus the optical performance analysis of the MDL under any error morphology has high applicability and accuracy. The present invention can obtain the performance loss of the MDL under the influence of this manufacturing process / this type of error morphology by fitting the error function ε, constructing an error model, and calculating the optical performance deviation rate, and then a more detailed tolerance range can be given to facilitate process improvement, which is highly practical. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 A schematic diagram of a multi-order diffraction lens for use in this embodiment;

[0032] Figure 2 This is a specific implementation flow chart of the patent of this invention;

[0033] Figure 3 (a) is a local enlarged view of the MDL concave step morphology; (b) is a schematic diagram of the discrete sub-circle distribution obtained by the error contour differential analytical method;

[0034] Figure 4 (a) is the height distribution of the ideal MDL morphology; (b) is the height distribution of the concave MDL morphology;

[0035] Figure 5 (a) is the relative focus position deviation rate under the influence of different sag rates e; (b) is the relative focusing efficiency deviation rate under the influence of different sag rates e. DETAILED DESCRIPTION

[0036] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the attached examples. Obviously, the described embodiments are only part of the embodiments of the present invention, which are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0037] The design principle of the present invention is: firstly, for the type of morphological error caused by MDL processing, an error function ε is constructed, and then for this type of error, an error function ε is constructed; then, based on the constructed error function ε, the MDL error height distribution matrix h is obtained. ij ; Then based on the obtained MDL error height distribution matrix h ij , calculate the light intensity distribution of MDL at the focal plane under the influence of its error; finally, calculate the relative focus position offset and relative focusing efficiency loss of MDL under the influence of the error.

[0038] This embodiment selects the MDL with actual ring concave error after processing and forming as the implementation object of the present invention. Figure 1 As shown, the MDL targeted by this embodiment is composed of several groups of circular rings, and the width of each circular ring is constant at w. After the optimization algorithm optimizes each ring belt, the heights are different, forming a set of ideal step height distribution matrices h related to the axial position. i Due to the existence of processing errors, the surface of the MDL ring step after forming deviates from the ideal flat morphology and has a certain concave error.

[0039] See also Figure 2 , a method for analyzing manufacturing errors of multi-order diffraction lenses based on annular zone reconstruction differentials, comprising the following steps:

[0040] Step 1: Construct the error function ε according to the type of morphological error caused by MDL processing:

[0041] like Figure 3As shown in (a), for the symmetrical MDL step depression morphology, a nonlinear regression model can be used to construct the error function ε:

[0042]

[0043] In formula (2), e is the concavity factor, and the maximum concavity degree of a single ring is Δh = h i ×e,j is the index value of the number of micromolecular rings p, that is, p = 1, 2, 3, ..., j; Figure 3 As shown in (b), when the number of sub-rings increases, the degree of error morphology restoration is higher, and the corresponding sub-ring width is w p =w / p.

[0044] Step 2: Based on the constructed error function ε, obtain the error height distribution h ij

[0045] For the ideal step height distribution matrix h i Perform matrix transformation based on the error function ε to obtain the concave step height distribution matrix h ij , error height distribution matrix h ij The error function ε and the initial height distribution h i It is obtained by matrix transformation, so it can more accurately describe the error shape of complexity. The formula is as follows:

[0046]

[0047] Figure 4 (a) shows the height distribution of the ideal MDL morphology. Figure 4 (b) shows the height distribution of the MDL concave morphology obtained by the mapping transformation based on the error function ε. After the error function ε matrix transformation, the dimension of the height distribution matrix containing the concave error information is expanded from i to i×j.

[0048] Step 3: Calculate the diffracted light field of the MDL at the focal plane under the influence of the error:

[0049] In actual operation, scalar or vector diffraction theory can be flexibly selected for calculation according to the limitation of computing resources. In this embodiment, in the rectangular coordinate system (x, y), the MDL height distribution function containing the concave error information is characterized as:

[0050]

[0051] Among them, ε(h i ) corresponds to the error mapping transformation of formula (1); ci rc() is the cylindrical function; Δh and Δw are the additional distortions in the axial and lateral directions of the ring, and are 0 if there is no additional distortion.

[0052] Accordingly, the MDL phase distribution containing notch error information is expressed as:

[0053]

[0054] Where α(λ)=k[n(λ)-1], k is the wave number, and n(λ) is the refractive index of the MDL at different operating wavelengths.

[0055] Therefore, the transmittance function containing error information is characterized as:

[0056]

[0057] Based on this, the light field distribution at the focal plane after a plane wave of unit amplitude irradiates the error MDL can be obtained using scalar or vector calculation methods. The calculation method for scalar diffraction theory is:

[0058]

[0059] Then the light intensity distribution curve at the MDL focal plane containing error information can be obtained:

[0060] I(x',y',λ,f)=|U(x',y',λ,f) 2 (3)

[0061] Step 4: Calculate the optical performance index of MDL under the influence of error:

[0062] Select the average focus position Average focusing efficiency As an evaluation indicator of performance loss under the influence of errors.

[0063]

[0064] Where: n is the total number of working wavelengths;

[0065] Average focus position Represents the achromatic performance index of MDL. The closer it is to the theoretical design value, the better the MDL achromatic effect is. For the average focal position in formula (4), the calculation method is the average of the maximum value position z of the axial light intensity I(z).

[0066] Average focusing efficiency Represents the quality of MDL focusing performance. The closer the value is to 1, the better the focusing performance of the surface MDL. For the average focusing efficiency, it is calculated as the average of the ratio of the optical power in the Airy disk area to the optical power within the MDL aperture range.

[0067] In order to better reflect the degree of performance loss, the relative deviation rates of the two compared to the theoretical values ​​are calculated respectively, namely:

[0068]

[0069] Figure 5 This is the result of the optical performance analysis of the MDL ring concave error based on the present invention. By performing error contour differential analysis on the error morphology of the MDL ring surface concave, it can be seen that the relative loss rate of the MDL optical performance is calculated by numerical calculation and simulation respectively. The numerical calculation results are consistent with the simulation results, showing that: with the increase of the concave rate e, the maximum relative focus position offset is about 20%, and the relative focusing efficiency loss is serious, up to about 60%.

[0070] The above is an explanation of the specific implementation of the present invention, rather than a limitation of the present invention. Those skilled in the relevant technical field can also make various equivalent technical solutions without departing from the scope of the present invention, so all equivalent technical solutions should be included in the patent protection scope of the present invention.

Claims

1. A method for analyzing manufacturing errors of multi-order diffraction lenses based on annular zone reconstruction differentials, characterized in that: The following steps are involved: Step 1: Construct the error function ε for the type of morphological error caused by MDL processing: Step 2: Based on the constructed error function ε, obtain the error height distribution h ij ; Step 3: Calculate the diffracted light field of the MDL at the focal plane under the influence of the error: Step 4: Calculate the optical performance index of MDL under the influence of errors.

2. The method for analyzing manufacturing errors of multi-order diffraction lenses based on annular zone reconstruction differential according to claim 1, characterized in that: In step 2, the ideal step height distribution matrix h i Perform matrix transformation based on the error function ε to obtain the concave step height distribution matrix h ij :

3. The method for analyzing manufacturing errors of multi-order diffraction lenses based on annular zone reconstruction differential according to claim 1 or 2, characterized in that: In the step 1, a nonlinear regression model is used to construct the error function ε: In formula (2), e is the concavity factor, and the maximum concavity degree of a single ring is Δh = h i ×e,j is the index value of the number of micromolecular rings p, that is, p = 1, 2, 3, ..., j; the width of the sub-ring is w p =w / p.

4. The method for analyzing manufacturing errors of multi-order diffraction lenses based on annular zone reconstruction differential according to claim 3, characterized in that: In step 3, the light intensity distribution curve at the MDL focal plane containing error information is: I(x',y',λ,f)=|U(x',y',λ,f) 2 (3)。 5. The method for analyzing manufacturing errors of multi-order diffraction lenses based on annular zone reconstruction differential according to claim 4, characterized in that: In step 4, the optical performance index includes the average focal position and the average focusing efficiency The relative deviation rate.

6. The method for analyzing manufacturing errors of multi-order diffraction lenses based on annular zone reconstruction differential according to claim 5, characterized in that: In step 4, the average focal position It is defined as the average value of the coordinates corresponding to the maximum axial (z-axis) light intensity I(z): The relative deviation rate compared to the theoretical value is:

7. The method for analyzing manufacturing errors of multi-order diffraction lenses based on annular zone reconstruction differential according to claim 5, characterized in that: In step 4, the average focusing efficiency It is defined as the average ratio of the optical power in the focal plane Airy disk area to the optical power within the MDL aperture: Where: n is the total number of operating wavelengths; The relative deviation rate compared to the theoretical value is:

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