Design of optical imaging system of fully automatic focal meter based on CCD

The focal meter studied in this paper is an automatic focal meter based on the projection principle. However, unlike similar domestic products, the automatic focal meter studied in this paper adopts a new mathematical model for measuring images, and its measurement accuracy and stability are greatly improved compared with similar domestic products.

1 Derivation of the optical algorithm of the fully automatic focal meter

1.1 Working principle of the fully automatic focal meter

Figure 1 is a schematic diagram of the optical path of the automatic focal meter. The light emitted by the point light source is collimated by the collimator, irradiated on the lens to be tested, deflected, and then projected onto the CCD through the beam splitter and the measuring lens. An image containing a mathematical model is obtained on the CCD. Due to the different refractive states of the tested lens, the size, position and shape of the image on the CCD will change. The relevant parameters of the tested lens can be obtained by receiving the CCD and processing the image position and shape by the microcomputer.

1.2 16-point mathematical model

Figure 2 is the image distribution diagram on the CCD when there is no measuring lens, that is, OD. When the measured lens is a negative spherical mirror, the sixteen light spots expand symmetrically relative to the initial position; when the measured lens is a positive spherical mirror, the sixteen light spots shrink symmetrically relative to the initial position. Divide the 16 light spots into four groups as shown by the dotted lines in Figure 3. Calculate the distance between the two image points in the X direction or the Y direction respectively, and you can get the vertex power S value of the measured spherical mirror. Assume that the vertex power values ​​obtained by the four groups of light spots are S1, S2, S3 and S4, then the S value is

When the lens under test is a cylindrical lens, the light spot distribution diagram on the CCD is shown in Figure 3. Since the cylindrical lens has two main vertex focal lengths, the 16 light spots are asymmetrically distributed. Taking one group of light spots (4 measurement points) as an example, the calculation method of the main vertex focal length of the cylindrical lens is derived. Let the distance between point A and point C in the X-axis direction be x2, and the distance in the Y-axis direction be y1; let the distance between point B and point D in the X-axis direction be x1, and the distance in the Y-axis direction be y2. Assume that D1 and D2 are the two main vertex focal lengths of the cylindrical lens, and θ is the axial angle of the cylindrical lens. The following equations hold

The calculation methods for the other three groups of light spots are the same as above and will not be repeated here. Suppose the vertex power values ​​of the cylindrical lens calculated by the four groups of light spots are C1, C2, C3 and C4, and the axis angles are θ1, θ2, θ3 and θ4, then the vertex power C value and axis angle of the cylindrical lens are

2 Image Processing System of Fully Automatic Lens Meter

The hardware system is designed according to the working principle of the automatic focal meter and the functions to be realized by the system. The system consists of two parts: data acquisition system and data processing system. The data acquisition system consists of CCD, A/D, AVR microcontroller and FIFO memory, which is mainly responsible for collecting data and storing it in FIFO memory; the data processing system consists of FPGA, LCD, FIFO memory, keyboard, and LED light source, which is mainly responsible for analyzing and calculating the collected data, and outputting the calculation results for display or printing.

CCD is a surface array sensitive element. During the integration time, charge accumulates on the CCD sensitive element. When the integration is completed, the charge data is shifted out in sequence. Since the charge data is a weak analog quantity, it must be amplified and then converted by A/D to obtain the digital quantity required by this system. In order to reduce the CPU occupancy rate of the FPGA, a memory is set on the CCD sampling board to temporarily store the converted data for the FPGA system to read. When there is no measuring lens in the optical path, the FPGA reads the collected data of the CCD, calculates the center position of the light spot, and uses the calculation result as the initial parameter of the system. When the measured lens is inserted into the optical path, the imaging position of the graticule on the CCD will change, and the change in position has a corresponding proportional relationship with the spherical and cylindrical powers of the measured lens. The FPGA receives the position information of the image and calculates the relevant parameters of the measured lens after transformation.

3 Image Binarization

It can be seen from the above system that the quality of image processing will directly affect the accuracy and stability of the measurement. Since the image acquisition device CCD adopts the PAL system, the system requires that the FPGA process a frame of image in no more than 20ms. The selection criteria for the image binarization algorithm are simple, effective and easy to implement. Therefore, this system adopts the maximum inter-class variance threshold segmentation algorithm. The basic idea of ​​the maximum inter-class variance method is to divide the pixels in the image into two categories A and B according to the grayscale value using the threshold t. A is composed of pixels with grayscale values ​​between 0-t, and B is composed of pixels with grayscale values ​​between t+1-L-1 (L is the grayscale level of the image). The inter-class variance between A and B is calculated according to the following formula.

Where wA(t) is the number of pixels in A, wB(t) is the number of pixels in B. uA(t) is the average grayscale value of all pixels in A, and uB(t) is the average grayscale value of all pixels in B. u(t) is the average grayscale value of the entire image.

Change the t value from 0 to L-1 in sequence, and take the t value that makes δ(t) the largest as the optimal threshold T.

Usually, the center coordinate of a light spot should be the center of the circle of the light spot. However, the image processed by FPGA is discretized and no longer arranged regularly, so the center of the light spot is calculated by the centroid calculation method. First, assume that the light spot is composed of n pixels, the spatial coordinates corresponding to each pixel are (xi, yi), and the gray value is p(xi, yi), then the centroid coordinates of the light spot are

Since xi and yi are the centroid coordinates of the FPGA memory image, they can be converted into the center coordinates of the light spot in the actual image through a certain equivalent conversion. Substituting the center coordinates of each point into equations (7)-(10), the relevant parameters of the tested lens can be obtained.

4 Conclusion

This paper proposes a new measurement image of the fully automatic focal meter and establishes the corresponding calculation method. The system is used to measure a series of standard lenses, and the technical indicators have reached the relevant national inspection standards.