An error analysis method for manufacturing multi-order diffraction lenses based on annular zone reconstruction differentiation

Abstract

This invention belongs to the field of multi-order diffractive lens (MDL) fabrication, specifically relating to a method for analyzing manufacturing errors of MDLs based on annular reconstruction differential. The method includes: firstly, constructing an error function ε to address the types of topographic errors caused by fabrication in the MDL; then, based on the constructed error function ε, obtaining the MDL error height distribution matrix h. ij Then, the diffraction field of the MDL at the focal plane is calculated; finally, the optical performance indicators of the MDL under the influence of errors are calculated, including relative focal position shift and relative focusing efficiency loss. This invention can effectively analyze the optical performance related to complex morphological errors formed during the MDL manufacturing process; it can accurately analyze the changing trend and range of optical performance loss of MDL under the influence of manufacturing errors through theoretical calculations and simulations; it has high applicability and accuracy in the optical performance analysis of MDL under arbitrary error morphologies; this invention facilitates process improvement and is highly practical.

Description

Technical fields:

[0001] This invention belongs to the field of multi-order diffractive lens processing, specifically relating to a method for analyzing manufacturing errors of multi-order diffractive lenses based on annular zone reconstruction differential. Background technology:

[0002] The design and application of broadband achromatic imaging devices has always been a research hotspot in the field of optical imaging. Traditional optical imaging systems generally adopt the following two schemes for achromatic imaging design: cementing multiple sets of positive and negative lenses of different materials, or a combination of refractive and diffractive lenses. Both of these achromatic schemes rely on traditional curvature lenses, which leads to the optical imaging system becoming redundant in size as achromatic performance improves, and the stacking of multiple lenses also increases the overall cost of system design.

[0003] Multi-level diffractive lenses (MDLs) are capable of achieving broadband achromatic focusing with a single lens. They consist of several sets of concentric rings of equal width. An optimization algorithm is used to find the optimal height distribution of each ring to provide target phase shift at different lens positions, enabling MDLs to achieve achromatic focusing of multiple incident wavelengths in the far-field target region.

[0004] Since the feature size of MDL (Medium-Density Array) is on the micrometer scale, most current manufacturing processes cause some distortion on the annular surface, resulting in error morphology. Related design studies both domestically and internationally have also shown that the actual performance of the manufactured MDL deviates significantly from the theoretical design values. Therefore, conducting relevant error analysis to improve lens design and manufacturing paths is of practical significance. Sourangsu Banerji et al. proposed an error analysis method for the annular height h and width w. By applying offsets Δh and Δw based on a normal distribution to each annular height or width, it can effectively solve for the optical performance loss caused by manufacturing process errors in the MDL annular height and width. However, since this error analysis method still only analyzes the original number of annular bands, it cannot effectively fit, model, and analyze more common and complex annular morphology errors in MDL. Summary of the Invention:

[0005] This invention provides a method for analyzing manufacturing errors of multi-order diffractive lenses based on annular reconstruction differential, in order to solve the problem of poor applicability of existing MDL manufacturing error analysis methods.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows: A method for analyzing manufacturing errors of a multi-order diffractive lens based on annular zone reconstruction differential, comprising the following steps:

[0007] Step 1: Construct an error function ε to address the morphological error types 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 diffraction field of MDL at the focal plane under the influence of calculation errors;

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

[0011] Furthermore, in step two above, the ideal step height distribution matrix h... i The height distribution matrix h of the concave steps is obtained by performing a matrix transformation based on the error function ε. ij :

[0012]

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

[0014]

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

[0016] Furthermore, in step three above, the light intensity distribution curve at the MDL focal plane, which includes error information, is as follows:

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

[0018] Furthermore, in step four above, the optical performance indicators include the average focal position. and average focusing efficiency The relative offset rate.

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

[0020]

[0021] The relative deviation from the theoretical value is:

[0022]

[0023] Furthermore, in step four above, the average focusing efficiency... Defined as the mean ratio of optical power within the Airy disk region of the focal plane to optical power within the MDL aperture region:

[0024]

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

[0026] The relative deviation from the theoretical value is:

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

[0028] 1. This invention seeks to identify the annular morphology errors caused by different MDL manufacturing processes, constructs an error function, and establishes an MDL error model by mapping the error function to an ideal height distribution. Subsequently, commonly used calculation methods can be selected to solve for the diffraction field distribution at the MDL focal point. Then, by calculating the optical performance loss of the MDL under the influence of errors (including relative focal point position shift and relative focusing efficiency loss), error analysis of MDLs of corresponding manufacturing processes / error types can be performed. Because a differential analytical operation is performed on the initial annulus, arbitrary error morphology distributions can be effectively approximated by controlling the height distribution of the sub-annulus. Therefore, this invention can effectively analyze the optical performance related to complex morphology errors formed during MDL manufacturing.

[0029] 2. Steps one and two of the present invention transform the abstract error morphology into a quantifiable subwavelength size structure by performing differential analysis on the error profile. This enables accurate analysis of the trend and range of optical performance loss of MDL under the influence of manufacturing errors through theoretical calculations and simulations.

[0030] 3. Since the error function ε in step two can be characterized by fitting methods such as nonlinear regression, and its specific form depends on the distribution of the ring band error height of a single ring (or the entire MDL) caused by various actual MDL processing techniques, it has high applicability and accuracy for optical performance analysis of MDL under arbitrary error morphologies. This invention, by fitting the error function ε, constructing an error model, and calculating the optical performance offset rate, can obtain the performance loss of MDL under the influence of this manufacturing process / error morphology, and thus provide a more detailed tolerance range to facilitate process improvement, making it highly practical. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the multi-order diffraction lens addressed in this embodiment;

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

[0033] Figure 3 (a) is a magnified view of the local morphology of the MDL concave steps; (b) is a schematic diagram of the discrete sub-ring distribution obtained by the error profile differential analytical method.

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

[0035] Figure 5 (a) represents the relative focus position offset rate under the influence of different indentation rates e; (b) represents the relative focus efficiency offset rate under the influence of different indentation rates e. Detailed implementation method:

[0036] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying embodiments. Obviously, the described embodiments are only some embodiments of this invention and are used only to illustrate the invention, but are not intended to limit the scope of the invention.

[0037] The design principle of this invention is as follows: First, for the type of topographic error caused by processing in MDL, an error function ε is constructed. Then, for this type of error, an error function ε is constructed again. Finally, based on the constructed error function ε, the MDL error height distribution matrix h is obtained. ij Based on the obtained MDL error height distribution matrix h ij The light intensity distribution of the MDL at the focal plane position under the influence of the error is calculated; finally, the relative focal position shift and relative focusing efficiency loss of the MDL under the influence of the error are calculated.

[0038] This embodiment selects an MDL (Medium-Density Detail) with actual annular concave errors after processing and forming as the object of implementation of the present invention. For example... Figure 1 As shown, the MDL in this embodiment consists of several sets of circular rings, each with a constant width w. After optimization by an algorithm, the heights of each ring are different, forming an ideal step height distribution matrix h related to the axial position. i Due to processing errors, the surface of the formed MDL annular step deviates from the ideal flat shape and has a certain degree of concavity error.

[0039] See Figure 2 A method for analyzing manufacturing errors of multi-order diffractive lenses based on annular zone reconstruction differential includes the following steps:

[0040] Step 1: Construct an error function ε to address the morphological errors caused by processing in MDL:

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

[0042]

[0043] In equation (2), e is the indentation factor, and the maximum indentation degree of a single ring is Δh = h. i ×e,j is the index value of the number p of the micro-molecule rings, i.e., p = 1, 2, 3, ..., j; for example Figure 3 As shown in (b), the more sub-rings there are, the higher the degree of error morphology restoration, 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 The height distribution matrix h of the concave steps is obtained by performing a matrix transformation based on the error function ε. ij Error height distribution matrix h ij The error function ε and the initial height distribution h i The matrix transformation is used to obtain the error profile, which can more accurately describe the complexity of the error. 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 topography obtained by the mapping transformation based on the error function ε. After the matrix transformation by the error function ε, the dimension of the height distribution matrix containing concave error information is expanded from i to i×j.

[0048] Step 3: Calculate the diffraction field of MDL at the focal plane under the influence of calculation errors:

[0049] In practice, scalar or vector diffraction theory can be flexibly selected for calculation based on computational resource limitations. In this embodiment, the MDL height distribution function containing concavity error information in the Cartesian coordinate system (x,y) is characterized as:

[0050]

[0051] Wherein, ε(h) i ) corresponds to the error mapping transformation of equation (1); ci rc() is the cylindrical function; Δh and Δw are the additional distortion variables of the annulus in the axial and transverse directions, respectively. If there is no additional distortion, then it is 0.

[0052] Accordingly, the MDL phase distribution containing concave error information is represented as:

[0053]

[0054] Where α(λ) = k[n(λ)-1], k is the wave number, and n(λ) is the refractive index of 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 is incident on the error MDL can be obtained using scalar or vector calculation methods. The calculation method for scalar diffraction theory is as follows:

[0058]

[0059] The light intensity distribution curve at the MDL focal plane, which includes error information, can then be obtained:

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

[0061] Step 4: Calculate the optical performance indicators of MDL under the influence of errors:

[0062] Selecting the average focal position Average focusing efficiency As an evaluation index for performance loss under the influence of errors.

[0063]

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

[0065] Average focal position This represents the color difference performance index of MDL. The closer it is to the theoretical design value, the better the MDL achromatic effect; for the average focal position of equation (4), the calculation method is the average value of the position z of the maximum value of axial light intensity I(z).

[0066] Average focusing efficiency This value represents the focusing performance of the MDL (Medium-Density Surface Layer); the closer the value is to 1, the better the focusing performance of the surface MDL. The average focusing efficiency is calculated as the average ratio of the optical power within the Airy disk region to the optical power within the MDL aperture region.

[0067] To better reflect the degree of performance loss, the relative deviation rates of the two values ​​from the theoretical values ​​are calculated, which are:

[0068]

[0069] Figure 5 This invention is based on the analysis results of the optical performance of MDL annular concavity error. By performing error profile differential analysis on the error morphology of the MDL annular surface concavity, it can be seen that the relative loss rate of MDL optical performance calculated by numerical calculation and simulation are consistent with the results of simulation, indicating that as the concavity rate e increases, the relative focal position shift is at most about 20%, and the relative focusing efficiency loss is severe, reaching a maximum of about 60%.

[0070] The above description is a specific illustration of the present invention, and not a limitation thereof. Those skilled in the art can make various equivalent technical solutions without departing from the scope of the present invention; therefore, all equivalent technical solutions should fall within the patent protection scope of the present invention.

Claims

1. A method for analyzing manufacturing errors of multi-order diffractive lenses based on annular zone reconstruction differential, characterized in that: Includes the following steps: Step 1: To address the morphological errors caused by the fabrication process in multi-order diffraction lenses, construct an error function ε: Step two, based on the constructed error function ε, get the error height distribution h ij ; Step 3: Calculate the diffraction field of the multi-order diffraction lens at the focal plane under the influence of calculation errors: Step 4: Calculate the optical performance indicators of the multi-order diffraction lens under the influence of errors; In step one, a nonlinear regression model is used to construct the error function ε: In equation (2), e is the indentation factor, and the maximum indentation degree of a single ring is Δh = h. i ×e,j is the index value of the number p of the micro-molecular rings, i.e., p = 1, 2, 3, ..., j; the width of the sub-rings is w. p =w / p,h i Ideal step height distribution matrix; w is the width of each ring; In step four, the average focal position Defined as the average value of the coordinates corresponding to the maximum axial (z-axis) light intensity I(z): Where n is the total number of working wavelengths; The relative deviation from the theoretical value is: Average focusing efficiency Defined as the average ratio of optical power within the Airy disk region of the focal plane to optical power within the aperture range of the multi-order diffraction lens: Where: n is the total number of working wavelengths; The relative deviation from the theoretical value is:

2. The method for analyzing manufacturing errors of a multi-order diffractive lens based on annular reconstruction differential as described in claim 1, characterized in that: In step two, the ideal step height distribution matrix h i The height distribution matrix h of the concave steps is obtained by performing a matrix transformation based on the error function ε. ij :

3. The method for analyzing manufacturing errors of a multi-order diffractive lens based on annular reconstruction differential as described in claim 2, characterized in that: In step three, the light intensity distribution curve at the focal plane of the multi-order diffraction lens, which contains error information, is as follows: I(x',y',λ,f)=|U(x',y',λ,f)| 2 (7) Where λ is the operating wavelength.

4. The method for analyzing manufacturing errors of a multi-order diffractive lens based on annular reconstruction differential as described in claim 3, characterized in that: In step four, the optical performance indicators include the average focal position. and average focusing efficiency The relative offset rate.

Images