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In the following article we will see how to perform the necessary calculations to design a mobile phone camera and I shall expose my own design of its own.
Designing a mobile phone camera phone is not a simple task. In this case we will design a system with a number f / 2.8 with a field of view of 76º.
The first thing to do is choose the sensor that we are going to use. In this case I have chosen the OV24B sensor. It is a 24 megapixel sensor with resolutions of 4K, 2K, 1080p and 720p. In Figure 1 we can see the product specifications.
Figure 1. Sensor specifications
Once the sensor is selected, we see that the pixel size is 0.9 microns, so the lateral color can not be larger than 0.9 microns. Looking at the area of the image, we can calculate the size of the image, since half of the diagonal of the image area will be the height of the final image.
Once we know the height of the image and knowing that the HFVO is 38º (half of the 76º of FOV), we can calculate the focal point by means of a simple trigonometric rule. Figure 1 indicates that the chief ray can not exceed 35.1º. This is very important to take into account when designing.
The MFT criterion is related to the Nysquit frequency of the sensor. In this case, the inverse of twice the size of the pixel will tell us the cutoff frequency. Also we are going to calculate the size of the Airy disk, because it will tell us what the maximum size of the Spot Size RMS should be.
The minimum relative illumination is calculated through the rule of cosine to the fourth. This is related to the angle of incidence (which we know because it is the HFVO). Table 1 in Figure 2 lists all results
Figure 2. Basic Calculation
Once we are clear about the objectives we have to achieve, we select the configuration of crystals we are going to use. In this case we will use 0G6P, 0 lenses and 6 plastic lenses. These plastic lenses allow us extreme aspherical shapes. In Figure 3 we have the system report.
Figure 3. Report of the system
The system consists of five lenses, the second being glass and the rest plastic lenses. The lenses used for this design are (in order); F52R-OKP4-COC-F52R-F52R-F52R-P_BK7. This last lens is the parallel flat plate that serves not only as a protector for the sensor, but also acts as an infrared filter.
The system finally has a focal length of 4.10 mm, 5.17 millimeters long, a f/2.8 number and the final image size is 3.20 mm.
As can be seen from the diagram of Seidel's aberrations, the predominant aberration has been distortion, although it was not difficult to compensate well. The size of the Spot Size RMS was more complicated to achieve.
In the FFT MTF graph we can see that at the spatial frequency of 223 cycles per millimeter the OTF module value corresponding to the diffraction limit is 0.54 (for both the tangential and sagittal plane values), this being the maximum figure that a perfect system would reach. The system presented reaches in axis an OTF module value of 0.48 (for both the sagittal and tangential planes). At mid-field, 20º the value of the OTF module is 0.40 for the tangential plane and 0.49 for the sagittal plane. At 38º degrees the value of the OTF module is 0.11 for the tangential plane and 0.41 for the sagittal plane. The system shows a really good performance. The tangential planes of the fields of 38º and 34º happen to show the poorest outcome. The performance of the system can also be seen in the PSF graph.
We had certain conditions to meet regarding side color value, relative illumination, and distortion.
The distortion is below 0.8% (when we had as top 1%) and the field curvature is less than 0.08 mm. At the bottom is the grid test graph to check for low system distortion.
The size of the Spot Size RMS is less than 4.4 microns in all fields. This assures us that the performance of the system will be excellent. From 20º we can see through the shape of the dot that there is a slight comma. However the size of the dot is smaller than Airy disk therefore the residual coma is coming up irrelevant.
At the bottom of the report we can check the graphics of the Tranverse Ray Fan and the OPD. The OPD graph has a scale of 0.5 waves, which indicates that the system is well optimized and has a good performance. In the graph of the RMS wavefront you can check again the quality of the system, being the polychromatism line below the diffraction limit line. In the graph of the lateral color, the scale is restricted to 0.9 microns, which is the maximum value we could reach, since the lateral color can not exceed the pixel size. In this case it is smaller, its maximum value being around 0.8 microns. The scale of the longitudinal aberration is very small and the three wavelengths pass at least twice through zero.
Another of the conditions that we had to fulfill was that, the chief ray did not surpass 35.1º (if we surpass this value the manufacturer of the sensor warns us that we are going to have vignetting and blurring in the images). In the graph "Incident Angle vs. Image Height" we can verify that we do not surpass 35.1º, staying in 35º in medium field, where we locate the maximum value.
As far as the relative illumination is concerned, we can see that it is decaying until it reaches the minimum permitted value of 38%. In the simulation of the image we see that the illumination actually decreases as we advance to the periphery. This lack of luminosity in the edge will be corrected later by the electronic circuit of the gain control.
In the graph "Diffraction Encircled Energy" and the PSF we see that almost all the irradiance falls on the first ring, as it should be , given that this is a system limited by diffraction.
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