Photometry with a color sensor 

Summary 🇫🇷  Traduire en français

• Introduction

• Description of the method

• Data used

• Calibration process

• Experimental results

• Conclusions

• Perspectives

1. Introduction

Color photometry using cameras with Bayer matrices is an accessible approach for measuring star magnitudes in three bands: B (blue), V (green), and R (red).

The Bayer colors of the sensor do not correspond exactly to the standard Johnson-Cousins filters, so our measurements must be converted.

The objective of this work is to propose a reliable and reproducible calibration method to derive standard magnitudes from the raw magnitudes obtained in each color channel. 

We use an OGMA color CMOS camera with a Bayer RGGB matrix (two green, one red, and one blue per 2×2 pixel square).

2. Description of the Method

The principle is based on extracting the raw V, B, and R layers, which we will call TG, TB, and TR, from the Bayer matrix.

After extraction, we compare these layers with reference stars obtained from an astronomical catalog. To retrieve them, we perform a Vizier query from the Strasbourg Stellar Data Center.

• Catalog used: "I/322A" (UCAC4).

• Columns used: "Vmag", "Bmag", "rmag".

Next, the principle relies on multiple linear regression using the raw magnitudes in the TG, TB, and TR channels to predict the standard V, B, and R magnitudes.

The calculation of Rmag is performed according to: Rc = r – 0.108 (B–V) – 0.132, where Rc represents the R magnitude corrected using the Johnson-Cousins system. This is an approximation to convert Sloan r magnitudes (SDSS or similar, such as those in UCAC4) into Rc (Cousins) magnitudes using the B−V color index. It is sufficiently precise for standard photometric work, as long as the color range remains moderate (typically 0<B−V<1.5).

This approximation is derived from an article published in The Journal of the British Astronomical Association (November 2018) by Roger Dymock & Richard Miles.

3. Data Used

Images: After selecting a star field containing Messier 36, the images are calibrated and aligned using ASTAP (Astrometric Stacking Program). For each image (separated into R, G, and B channels), we apply aperture photometry:

Measurement of the flux of each star

Subtraction of the background sky

Extraction: CSV files are generated for each channel (TG, TB, TR).

Content: Star coordinates and raw magnitudes (TG, TB, TR). For example:

• For exemple :
  053731.2+341622 11.568 11.580 11.539 11.536 11.568 11.557 11.558 11.562 11.563 11
  053633.3+342231 12.052 12.059 12.032 12.024 12.046 11.999 11.965 12.033 12.025 12

• Filtering: Removal of saturated or variable stars. 

4. Calibration Process

• Extract R, G, and B separately from the Bayerized image.

• Perform photometry (flux measurement) on each layer.

• Calculate instrumental magnitudes.

• Use standard stars to calibrate in the Johnson-Cousins system (color corrections).

• Apply conversion formulas.

• Execute multiple linear regression.

• Display the coefficients.

• Graphical visualization: measured vs. predicted TG + residual analysis.

Possible save options:

• Coefficients in a TXT file.

• Results in an Excel file (XLSX).

• Graphs in PNG format.

Since Bayer bands do not perfectly match Johnson-Cousins bands, color transformations must be applied. In general, formulas of the following type are used: 

V = G + a × (G−R) + b
B = B + c × (B−G) + d
R = R + e × (G−R) + f

Where: 

G, R, and B are the magnitudes measured on the sensor.

a, b, c, d, e, and f are empirically adjusted coefficients. 

6. Experimental Results

Number of stars used: 120. 

Obtained coefficients 

Regression TG → V

a = 0.939425

b = 0.598694

R² = 0.969082

RMSE = 0.125562

Regression TB→B

a = 0.922228

b = 1.219822

R² = 0.822156

RMSE = 0.317603

Regression TR→Rc

a = 0.946258

b = 0.305605

R² = 0.981768

RMSE = 0.104265

Qualitative Interpretation 

Canal Correlation (R²) Precision (RMSE) Overall Quality 

TG → V ★★★★★ (0.969) ★★★★☆ (0.126) Very good

TB → B ★★★★☆ (0.822) ★★★☆☆ (0.318) Moderately good 

TR → Rc ★★★★★ (0.982) ★★★★★ (0.104) Excellent

Quality of the TB → B Regression

The blue channel (TB → B) is clearly the least efficient (R² = 0.82, RMSE = 0.32). The examination of corrected residuals and the regression clearly shows a relative dispersion of the measurements. This is likely due to:

• Lower sensitivity of the Bayer blue channel.

• Higher noise levels in this band.

• Stronger atmospheric effects in B.

7. Conclusions

The proposed method allows for precise photometric calibrations from unfiltered Bayer images. In particular, for amateur photometry, the use of the V channel appears to be quite suitable. 

8. Perspectives

• With the regression coefficients now known, corrections can be made directly without relying on the Vizier server from the Stellar Data Center.

• Full automation of batch processing.

• Extension to other types of sensors.

• Comparison with standard calibrations from other software.