Calibration Method for the Wavelength and Uniformity of Pixel Response in Photodetector Arrays

EQ-99 is a laser-driven light source UV–VIS–NIR manufactured by ENER-GETIQ. This broadband source is specially designed for high brightness and high stability. The spectral output ranges from 170 to 2,100 nm, with a numerical aperture up to 0.47 and a typical bulb life longer than 5,000 hr. For the method presented in this paper it is crucial that the light source shows a flat spectral response, in such a way that the power is uniformly distributed in all the components of the visible spectrum, to ensure the presence of all the monochrome bands in the spectrum.

It is very important to use in the process a source capable of producing a continuous spectrum in the VIS with a output power close to uniform.

Mini-Chrom is a monochromator that uses a dial to select the output wavelength. A screw bar mechanism accurately guides the rotation of a diffraction grating, which positions the selected wavelength in the output. The wavelength is read directly in nanometers (nm) by a four-digit counter in all models. The operating range is 200 to 800 nm. SMA connectors will be adapted at the input and output for connecting plastic optical fibers, it is also possible to adapt a slit to the output. In the method presented in this work the output is open, and the camera surface is illuminated with the light coming out of the slit.

AQ6373 is a Spectrum Analyzer that provides an accurate high-speed analysis for a wavelength range between 350 and 1,200 nm. This optical spectrum analyzer (OSA) is well suited for general purposes. It also allows USB storage to save data in .csv format for further analysis. The resolution can be varied from 0.02 to 10 nm, or 0.01 nm for 400 to 470 nm range. Additionally, the AQ6373 has an optical alignment source.

FL3-U3-13Y3M-C (Fig. 1) is a monochromatic camera developed by FLIR with excellent performance. One of the main advantages of this type of cameras compared to those with domestic use is the availability of data in raw format. This allows one to directly obtain the response of the sensors without processing, and this is a necessary characteristic to use the camera as a measuring element, and all control parameters are known and operated manually.

Fig. 1

In Figure 2 the explanatory diagram of the proposed experiment is presented and its parts are described below:

The initial response value to obtain the saturation parameters is adjusted with light emitted at 525 nm.

Fig. 2

The compressed image storage formats make undetectable the defects on the sensors, because the processing operations repair or camouflage the pixels with information from the region. For this reason, the images used in this experiment are acquired in raw format due to the camera is used as a measurement element.

The method proposed in this work provides information on the operation of the sensor. The quality of the parameters must be adjusted for each experiment where the camera is used as a measurement element. For example, the number of defective pixels tolerated is a dependent value in the application. The images obtained using the experiment described in the previous subsection can be calibrated with the three steps process described below:

First, the mean and standard deviation are calculated for each of 105 images acquired in the experiment . The average value of the images reflects the power absorbed by the photodetectors array; however, the values in defective pixels are deviated considerably of the average.

In this step, pixels with two deviations above or below of the mean are selected as defective pixels. Defective pixels must be aligned between images with different angles to decrease the error in the experiment. These pixels do not provide information to the image, their response does not change to different stimulus, or it is substantially different to the rest of pixels.

In order to determine defects on the sensor surface, the mean and standard deviation of the response values for each image are calculated. Then, the pixels with two deviations above or below of the mean are selected. The results are shown in Figure 3, where P1, P2, and P3 are rotation positions, the images are shown for two wavelengths 460 and 740 nm. The white regions in the figure highlight the defective pixels, 227 defective pixels were detected. The purpose of camera rotation is that defective pixels appear in the same region facilitating their localization, and other regions produced by other different phenomena are discarded. The set of highlighted pixels must be excluded when the sensor is used as a measurement element. It is important to note that the images have artificial color to facilitate their interpretation.

Fig. 3

Figure 4 shows the raw response of the photodetector for different rotation positions (P1 and P5) and different wavelengths (480 and 640). These rotation positions were located equidistantly over 300 grades. The number of rotations positions can be increased up to the encoder resolution of the servomotor. The 10 bits encoder allows 1024 rotation positions between 30 and 330 grades, i.e., it is possible to acquire images each 0.29 grades, but this increase the time of recording.

In total the five images of each wavelength are averaged to calculate the resulting image Pm. It can be seen that uniformity improves. On this image, the response range for each wavelength is estimated.

Fig. 4

Measurements of spectra were taken every 20 nm in the range between 380 and 780 nm having 21 spectra in total. The uncertainty due to the orthogonality of the sensor plane when is illuminated, and nonuniformity of light of the monochromator output is reduced repeating the measurement five times in different angles. As shown in Figure 5, the spectra are narrow allowing improve the estimation of the generated response model. In addition, as mentioned in the description of the experiment the camera is moved near or far of the monochromator as appropriate to match with the power at 525 nm for each wavelength with the help of the spectrometer.

The mean of each image in each rotation position is obtained in this step and the mean for each evaluated wavelength of each rotated images is represented by the red dots, see Figure 6.

Eq. (1) presents the estimated sensitivity function of the camera (blue line in Fig. 6), where the parameter k must be adjusted with the power. k is a scale factor so that pixels respond proportionally, for this reason, this must be adjusted whenever the power changes to maintain the desired proportional response. (1) S(λ)=k⋅(1.2E−08⋅λ4−2.8E−05.λ3+0.02⋅λ2−5.7⋅λ+544.4).

Finally, in Table 1, the average value of each image for each position (P1, P2, P3, P4, P5) and each of the 21 sampled wavelengths is presented. The value is normalized from 0 to 100%, the last column shows the response range of the camera (margin).

Fig. 5

Fig. 6