## 2. **Breadboard Design and Implementation**
### Estimating the Limiting Magnitude of the Sensor  
The limiting magnitude is the maximum threshold value that the sensor can detect, i.e., the minimum brightness. In other words, this magnitude will provide the minimum size of detectable debris. To estimate the limiting magnitude, it is necessary to have information on the sources' brightness in specific wavebands relative to standard stars and the quantum efficiency of the sensor for different wavelengths.  
The Johnson-Cousins filters system was used as the information on the flux calibration of A0-type main-sequence stars for the distinct wavebands that the sensor can detect, namely blue (B), visible (V), red (R), and near-infrared (I) [18]. Also, the spectral sensitivity curve, present in the sensor datasheet [19], provides the values of the sensor quantum efficiency (\(QE\)) in different wavelengths. Therefore, the A0 star flux \(\Phi_{0}\) measured by the sensor is given by [18]:  
\[\Phi_{0}=\sum_{x=B,V,R,I}\Phi_{x}FWHM_{x}QE_{\lambda_{x}} \tag{6}\]  
Thus, the flux is the summation of the flux in different wavebands times the FWHM and quantum efficiency of each waveband as described in (6). After that, the magnitude \(m\) is determined by comparing the flux of a standard star, with a well-known magnitude, and the flux of the object of interest:  
\[m-m_{0}=-2.5\log\biggl{(}\frac{\Phi}{\Phi_{0}}\biggr{)} \tag{7}\]  
Figure 5: Camera in the interferometer (**a**); image of the light beam focused on the sensor with a horizontal intensity per pixel cut shown (**b**).  
In (7), the index 0 represents the standard star. Rearranging this equation, the flux for different magnitudes is given by:  
\[\Phi=\Phi_{0}\;10^{-\frac{m-m_{0}}{2\text{ s}}} \tag{8}\]  
Thus, (8) provides the flux in \(\frac{W}{m^{2}}\) for several values of magnitudes. The flux unit was converted to photons/m\({}^{2}\) by dividing each waveband flux by its photon energy. Then, our lens's transmission coefficient, which is 0.7, and its aperture area, as seen in Section 2.1, are multiplied in the outcomes. Hence, the flux has units of photons/s. Therefore, the sensor signal for different magnitudes was obtained by multiplying this result by the integration time. Thereby, signal and total noise values were used to determine the signal-to-noise ratio (SNR) [20]:  
\[SNR=\frac{N_{*}}{\sqrt{N_{*}+n_{pix}\big{(}N_{SN}+N_{DN}+N_{RN}^{2}\big{)}}} \tag{9}\]  
In (9), \(N_{*}\) is the signal and \(n_{pix}\) is the number of pixels considered for the calculation, which was 16 (FWHM calculated in Section 2.2). \(N_{SN}\) is the shot noise and is calculated by the square root of the signal. Also, the results estimated in Section 2.2 for the readout noise, \(N_{RN}\), and the dark noise, \(N_{DN}\), were applied in the SNR calculation.  
We considered the canonical \(SNR=5\) as the reliable detection limit, i.e., a detection is only reliable when its signal is five times higher than the noise levels. Therefore, for three integration times of 1 s, 3 s, and 5 s, the maximum detection magnitudes, i.e., the magnitudes of the faintest detectable objects/stars, were approximately 10.2, 11.4 and 11.9, respectively.