Systems and methods for estimating modulation transfer function in an optical system
A method of determining a modulation transfer function (MTF) for an image includes receiving an image captured through the optical system, performing edge detection on columns or rows in the image to calculate a plurality of edge points, calculating a plurality polynomials to fit to the calculated edge points, each of the plurality of polynomials varying in degree, selecting a polynomial from the plurality of polynomials to represent the detected edge, and estimating the MTF based on the selected polynomial.
1. A method of determining an optical system modulation transfer function (MTF) based on an image captured through the optical system, comprising:
receiving an image captured through the optical system;
performing edge detection on columns or rows in the image to calculate a plurality of edge points;
calculating a plurality polynomials to fit to the calculated edge points, each of the plurality of polynomials varying in degree;
selecting a polynomial from the plurality of polynomials to represent the detected edge by:
determining a residual error value for each of the plurality of polynomials;
determining a difference in the residual error value between each of the plurality of polynomials; and
selecting a highest degree polynomial among the plurality of polynomials that results in decrease in the residual error value less than a threshold amount;
estimating the MTF based on the selected polynomial; and
configuring a configuration of the optical system based on the estimated MTF.
2. The method of claim 1 , wherein the selected polynomial has a
degree higher than a second degree.
3. The method of claim 2 , further comprising binning the edge point data such that the line spread function has a resolution that is at least four times higher than original data from the image.
4. The method of claim 1 , wherein estimating the MTF comprises:
creating a line spread function based on the selected polynomial; and
binning edge point data of the line spread function.
5. The method of claim 1 , wherein the edge is a concave edge.
6. The method of claim 1 , wherein the edge is a circular edge.
7. The method of claim 1 , wherein the edge is an arbitrary smooth edge.
8. A system, comprising:
a memory storing instructions;
a processor configured to execute a process on a digital image captured by an optical system based on the instructions, the process including the operations of:
an image captured through the optical system;
performing edge detection on columns or rows in the image to calculate a plurality of edge points;
calculating a plurality polynomials to fit to the calculated edge points, each of the plurality of polynomials varying in polynomial degree;
selecting a polynomial from the plurality of polynomials to represent the detected edge by:
determining a residual error value for each of the plurality of polynomials;
determining a difference in the residual error value between each of the plurality of polynomials; and
selecting a highest degree polynomial among the plurality of polynomials that results in decrease in the residual error value less than a threshold amount;
estimating the MTF based on the selected polynomial; and
configuring a configuration of the optical system based on the estimated MTF.
9. The system of claim 8 , wherein the selected polynomial has a
degree higher than a second degree.
10. The system of claim 8 , wherein the operation of estimating the MTF comprises:
creating a line spread function based on the selected polynomial; and
binning edge point data of the line spread function.
11. The system of claim 10 , the process further comprising binning the edge point data such that the line spread function has a resolution that is at least four times higher than original data from the image.
12. The system of claim 8 , wherein the edge is a concave edge.
13. The system of claim 8 , wherein the edge is a convex edge.
14. The system of claim 8 , wherein the edge is a circular edge.
15. The system of claim 8 , wherein the edge is an arbitrary smooth edge.
16. A system, comprising:
a memory storing instructions;
a processor configured to execute a process on a digital image captured by an optical system based on the instructions, the process including the operations of:
receiving the digital image captured by the optical system;
performing edge detection on columns or rows in the digital image to calculate a plurality of edge points;
calculating a current polynomial to fit to the calculated edge points;
determining a residual error value for the current polynomial;
performing a polynomial selection process by:
calculating a next polynomial to fit to the calculated edge points, the next polynomial having a greater polynomial degree than the current polynomial;
determining a residual error value for the next polynomial;
in response to a difference in the residual error values of the current and next polynomials being less than a threshold amount, selecting the current polynomial and ending the polynomial selection process; and
in response to the difference being greater than or equal to the threshold amount, assigning the next polynomial as the current polynomial and repeating the polynomial selection process;
estimating the MTF based on the selected polynomial; and
configuring a configuration of the optical system based on the estimated MTF.