CN114741812A - Aspheric lens design method based on differential rendering - Google Patents

Abstract

The invention discloses a design method of an aspheric lens based on differential rendering. The method comprises the following specific steps: (1) modeling the aspheric lens by using a spherical equation containing a correction factor, and then obtaining a corresponding three-dimensional model by using a Poisson surface reconstruction algorithm; (2) loading the three-dimensional model corresponding to the aspheric lens into a ray tracing-based differentiable rendering system, and rendering a generated image of a preset scene after passing through the aspheric lens; (3) perfecting an internal calculation chart of the differentiable rendering system, and establishing a mapping relation between a generated image and an aspheric lens design parameter; (4) and calculating loss functions of the generated image and the reference image, and optimizing design parameters of the aspheric lens by a gradient descent method. The method is based on the idea of ray tracing and gradient optimization, and the design method of the aspheric lens which does not need to depend on paraxial optics and has strong expansibility is realized.

Description

Aspheric lens design method based on differential rendering

Technical Field

The invention relates to the field of computational photography and computer graphics, in particular to a design method of an aspheric lens based on differential rendering.

Background

In recent years, aspherical lenses have been widely used in products such as camera lenses, spectacles, and optical read/write heads. The most significant advantage of an aspheric lens over a spherical lens is that the spherical aberration introduced by a spherical lens in the collimating and focusing system can be corrected. By adjusting the surface constant and the aspheric coefficient, the aspheric lens can eliminate spherical aberration to the maximum.

The existing aspheric lens design method is generally based on optical design software such as ZEMAX and Code V to optimize point spread functions corresponding to different areas or depths. The design method emphasizes direct optimization of the shape of the point spread function, and omits the application scene and the imaging quality of the lens.

Disclosure of Invention

In view of the above drawbacks of the conventional aspheric lens design method, the present invention provides a design method for an aspheric lens based on differential rendering.

In order to achieve the purpose, the technical scheme adopted by the invention is as follows:

a design method of an aspheric lens based on differential rendering comprises the following steps:

step 1, modeling an aspheric lens by using a spherical equation containing a correction factor, and then obtaining a corresponding three-dimensional model by using a Poisson surface reconstruction algorithm, wherein the spherical equation containing the correction factor is used for calculating the spatial coordinates and normal vectors of each sampling point on the aspheric lens surface, and the Poisson surface reconstruction is used for solving the lens surface corresponding to the sampling point;

step 2, loading the three-dimensional model constructed in the step 1 into a differentiable rendering system based on ray tracing, and rendering a generated image of a preset scene after passing through an aspheric lens;

step 3, perfecting an internal calculation graph of the differentiable rendering system, and establishing a mapping relation between a generated image and design parameters of an aspheric lens;

and 4, calculating loss functions of the generated image and the corresponding reference image, and optimizing design parameters of the aspheric lens by a gradient descent method.

The method simulates the behavior of light in the real world and the interaction process with an imaging system through ray tracing, and obtains the rendering result of a scene after passing through an aspheric lens; then, by means of the characteristics of a differentiable rendering system, the gradient of the rendering result relative to the design parameters of the aspheric lens is obtained; and finally, optimizing design parameters according to the average absolute error of the generated image and the reference image based on a gradient descent method. Compared with other existing aspheric lens design methods, the method gets rid of the assumption of paraxial approximation, and can obtain a more real and accurate imaging result; the invention has high expansibility and can embed a corresponding image reconstruction module according to an application scene.

Drawings

FIG. 1 is a flow chart of the method of the present invention;

FIG. 2 is a training flow diagram of one embodiment.

Detailed Description

The invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

Referring to fig. 1 and 2, a method for designing an aspheric lens based on differential rendering according to this embodiment includes the following specific steps:

step 1, modeling an aspheric lens by using a spherical equation H containing a correction factor, and then obtaining a corresponding three-dimensional model by using a Poisson surface reconstruction algorithm phi, wherein the former calculates a space coordinate V and a normal vector N of a sampling point on the lens surface, and the latter solves a lens surface F corresponding to the sampling point.

Given a cartesian coordinate system (x, y, z), the z-axis coincides with the optical axis, and (x, y) constitutes a plane perpendicular to the optical axis, where p is x²+y²The spherical equation with the correction factor is as follows:

wherein c represents an aspherical lens surfaceWith κ representing the conic coefficient, a_2iRepresenting higher order coefficients in the correction factor. The Poisson surface reconstruction algorithm is a reconstruction method combining the advantages of global matching and local matching, and the core idea is to construct an implicit surface with high fitting degree by converting discrete sampling point information of the surface of an aspheric lens into a continuous integrable surface function.

This embodiment first uniformly samples N on the entrance pupil plane with diameter D_sampleThe point, spherical equation H containing correction factor, obtains the coordinate z of each sampling point on the optical axis according to the coordinates (x, y) of each sampling point on the entrance pupil plane, and is specifically expressed as

z＝H(x,y,θ)

Here, θ denotes an initial design parameter of the aspherical lens. Then, a normal vector n corresponding to each sampling point can be solved according to the implicit equation of the aspheric lens, which is specifically expressed as:

f(x,y,z)＝H(x,y,θ)-z

after the calculation is finished, obtaining the space coordinates V and normal vectors N corresponding to all sampling points, wherein the respective sizes are N_sample×3。

And solving a lens surface F consisting of triangular surface patches by adopting a Poisson surface reconstruction algorithm phi according to the calculated sampling point information:

F＝Φ(V,N)

the poisson reconstruction surface algorithm is the prior art, and is not described in detail. Finally, the three-dimensional model corresponding to the aspheric lens is composed of { V, N, F } and is stored as a geometric figure file format OBJ, so that the subsequent program reading and writing operation is facilitated.

And 2, loading the three-dimensional model constructed in the step 1 into a ray tracing-based differentiable rendering system, and rendering a generated image of a preset scene after the preset scene passes through an aspheric lens.

First, several RGB images with 2048 × 1080 size are selected from the DIV2K dataset and randomly cropped into multiple RGB images with 128 × 128 size to serve as reference images.

And then, building a three-dimensional preset scene in a differentiable rendering system, specifically, placing a rectangular plate taking the RGB image as a texture mapping at the origin of a space coordinate system, taking two surface light sources as main light sources of the scene, and taking an image generated on a sensor after the texture mapping of the rectangular plate passes through an aspheric lens as an output result.

The differentiable rendering system includes: the aspheric lens module is used for reading the three-dimensional model corresponding to the aspheric lens and placing the three-dimensional model between a preset scene and the sensor; and the pixel coloring module is used for emitting light rays from the pixels of the sensor, tracking the paths of the light rays passing through the preset scene to calculate the color of the corresponding pixels, and rendering the generated image of the preset scene after passing through the aspheric lens. The differentiable rendering system takes into account reflection and refraction phenomena that rays may encounter during propagation, and thus can render accurate shadows, recursive reflections and refractions. The working principle makes the design method of the embodiment get rid of the assumption of paraxial approximation, and can consider the aberration of the paraxial and the abaxial simultaneously.

Here, the image information I generated by the sensor may be specifically expressed as:

I(x,y)＝∫Q(λ)·[p(x,y,d,λ)*s(x,y,d)]dλ+n(x,y)

the point spread function p (x, y, d, λ) is a function of the spatial location (x, y) on the sensor, d is the depth of the scene, and the incident spectral distribution. Q is the sensor spectral response value, and s (x, y, d) and (x, y) represent the implicit representation of the scene and the metric noise, respectively. Operator denotes convolution.

Step 3, perfecting an internal calculation graph of the differentiable rendering system, and establishing a mapping relation between a rendering result and lens design parameters such as curvature, cone coefficient and the like; the method specifically comprises the following steps:

firstly, through analyzing a calculation chart established by an aspheric lens module and a pixel coloring module in the system, the image is found to be read only by the calculation chart, and the generated image I only can be read according to the gradient of each vertex position V on the aspheric lens

Then, according to the spherical equation containing the correction factor in step 1, a mapping relation is established for the vertex position V of the aspheric lens and the design parameter theta:

V＝H(θ)

θ＝{c,κ}

an indirect mapping relation is established between the generated image and the design parameters of the aspheric lens through a chain rule:

finally, gradient return from the generated image to the aspheric lens design parameters is realized, and the lens design parameters are conveniently and continuously updated in iteration.

And 4, calculating a loss function of the generated image and the reference image in the image comparison module, then calculating the gradient of the loss function relative to the design parameters of the aspheric lens in the parameter updating module, and finally performing iterative optimization on the design parameters of the aspheric lens through a gradient descent method. The loss function used in this embodiment is the L1 loss function, i.e., the average absolute error.

LOSS＝||I-I_ref||₁

Where I is the image of the scene generated on the sensor after passing through the lens, I_refIs the corresponding reference picture.

Claims (6)

1. A method for designing an aspheric lens based on differential rendering is characterized by comprising the following steps:

step 1, modeling an aspheric lens by using a spherical equation containing a correction factor, and then obtaining a corresponding three-dimensional model by using a Poisson surface reconstruction algorithm, wherein the spherical equation containing the correction factor is used for calculating the spatial coordinates and normal vectors of each sampling point on the aspheric lens surface, and the Poisson surface reconstruction is used for solving the lens surface corresponding to the sampling point;

step 2, loading the three-dimensional model constructed in the step 1 into a differentiable rendering system based on ray tracing, and rendering a generated image of a preset scene after passing through an aspheric lens;

step 3, perfecting an internal calculation graph of the differentiable rendering system, and establishing a mapping relation between a generated image and design parameters of an aspheric lens;

and 4, calculating loss functions of the generated image and the corresponding reference image, and optimizing design parameters of the aspheric lens by a gradient descent method.

2. An aspheric lens design method based on differential rendering as claimed in claim 1, characterized in that in step 1, a cartesian coordinate system (x, y, z) is given, the z-axis coincides with the optical axis, (x, y) forms a plane perpendicular to the optical axis, and p ═ x²+y²The spherical equation with the correction factor is as follows:

where c denotes the central curvature of the aspherical lens surface,. kappa.denotes the conic coefficient,. a_2iRepresenting higher order coefficients in the correction factor.

3. The method as claimed in claim 1, wherein in step 1, the poisson surface reconstruction algorithm transforms discrete sampling point information of the aspheric lens surface onto a continuously integrable surface function, so as to construct an implicit surface with a high fitting degree.

4. The method as claimed in claim 1, wherein in step 2, the ray tracing-based aspheric lens design system comprises:

the aspheric lens module is used for reading the three-dimensional model corresponding to the aspheric lens and placing the three-dimensional model between a preset scene and the sensor;

and the pixel coloring module is used for emitting light rays from the pixels of the sensor, tracking the paths of the light rays passing through the preset scene to calculate the color of the corresponding pixels, and rendering the generated image of the preset scene after passing through the aspheric lens.

5. The method of claim 4, wherein in step 3, the step of refining the internal computation graph of the differential rendering system is as follows:

firstly, through analyzing a calculation chart established by an aspheric lens module and a pixel coloring module in the system, the image is found to be read only by the calculation chart, and the generated image I only can be read according to the gradient of each vertex position V on the aspheric lens

Then, according to the spherical equation containing the correction factor in step 1, a mapping relation is established for the vertex position V of the aspheric lens and the design parameter theta:

V＝H(θ)

θ＝{c,κ}

an indirect mapping relation is established between the generated image and the design parameters of the aspheric lens through a chain rule:

finally, gradient return from the generated image to the aspheric lens design parameters is realized, and the lens design parameters are conveniently and continuously updated in iteration.

6. The method of claim 1, wherein in step 4, the optimization of aspheric lens design parameters is constrained by mean absolute error:

LOSS＝||I-I_ref||₁

wherein, I is the scene passing through the aspheric lensImage generated on the sensor, I_refIs the corresponding reference picture.

Images