Lab 01: Detector Calibration

Apparatus and Setup

You will calibrate five real 40×40 pixel patches from an actual imaging session: a Canon EOS M50 (CMOS, RGGB Bayer, 14-bit ADC) on a William Optics Zenithstar 73 refractor with a Flat73R 0.8× reducer and an Astronomik CLS light-pollution clip filter, captured with BackyardEOS and calibrated with Astro Pixel Processor on 2022-07-19. The light frame is LIGHT_300s_400iso_+31c_20220719-22h40m39s641ms.CR3 (ISO 400, 300 s exposure). Because the session's master dark was built from four 300.1 s exposures — matching the light frames' exposure length — it already contains the bias pedestal, so calibration here uses a single dark-frame subtraction rather than separate bias and dark terms (see Lecture 1).

• Matched-exposure master dark level (green/G1 channel, from MD-IG_400.0-E300.100006s-CANON_EOS_M50-6288x4056-all_channels-session_1.fits, N = 4 frames): D = 2046.0 ± 1.32 ADU.
• For comparison, the separate master bias level (from MB-IG_400.0-E_2.5E-4s-...fits, N = 20 frames): B = 2047.6 ± 1.71 ADU — note D and B are statistically indistinguishable in mean level, confirming negligible mean dark current at this ISO and exposure length.
• Five source-patch raw ADU values (mean pixel value in each 40×40 patch) and their per-patch normalized flat-field values (from the matching master flat, MF-IG_400.0-E_0.3s-...fits, N = 19 twilight-sky frames), listed in the Materials table below.

Materials and Data

Worked check (do not simply copy — reproduce the arithmetic yourself before trusting it): for the top-left patch, I_cal = (2885.87 − 2046.0) / 0.96 = 874.9 ADU. For the center patch, I_cal = (3048.14 − 2046.0) / 1.09 = 919.4 ADU.

Procedure

1. Record the matched-exposure master dark value and its uncertainty in your notebook, along with the light frame's exposure length and ISO.
2. For each of the five patches, apply I_cal = (I_raw − D) / F and complete the calibrated-value column.
3. Estimate the uncertainty on each calibrated value from the master dark's own noise, propagated through the flat division: σ(I_cal) ≈ σ_D / F. Compute this for at least two patches and comment on whether it is the dominant uncertainty source (compare to Lecture 4’s Poisson term for a count level of a few hundred ADU above the calibration floor).
4. Plot calibrated ADU against patch position (top-left, top-right, center, bottom-left, bottom-right) and describe the pattern you see across the frame.
5. The camera's bad-pixel map (from the same 2022-07-19 calibration set) flags 2.554% of all pixels as "hot" and 4.882% as "cold." For a circular photometric aperture of 9 pixels (used in later labs), estimate the expected number of flagged pixels landing inside a randomly placed aperture, assuming pixels are flagged independently at these rates.
6. Write a two-to-three sentence conclusion stating which effect (vignetting/flat-field variation across the frame, or the dark-frame subtraction) changed each patch's value the most, and why a bad-pixel map is still needed even after dark and flat calibration.

Analysis and Uncertainty

The normalized flat value varies by roughly 10–13% across these five patches (0.90 to 1.09), while the dark-frame subtraction changes every patch by essentially the same fixed amount (about 2046 ADU). State explicitly, with a number, which correction (the flat's spatial variation, or the dark subtraction) dominates the patch-to-patch differences you observe in I_cal.

Deliverables

• Completed five-row calibration table with uncertainties.
• One plot or labeled diagram of calibrated ADU by patch position across the frame.
• The expected-flagged-pixel calculation for a 9-pixel aperture.
• A short (150–250 word) conclusion identifying the dominant spatial effect and explaining the continued need for a bad-pixel map.

Assessment Criteria

• Correct arithmetic and units for all five patches (matches or is consistent with the two worked checks).
• Uncertainty propagation shown explicitly, not just asserted.
• Expected flagged-pixel count is computed correctly from the stated hot/cold pixel fractions.
• Conclusion is evidence-based and references the actual computed numbers, not a generic statement.

References and Provenance

• OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e.pdf), Chapter 6.3 (visible-light detectors and instruments).
• Real calibration data: Canon EOS M50 imaging session, 2022-07-19, BackyardEOS capture and Astro Pixel Processor master-frame reduction; raw light frame and master bias/dark/flat/bad-pixel-map FITS files under C:\Users\rober\OneDrive\Pictures\BackyardEOS\2022-07-19\ and 00Masters\, logged with exact patch pixel coordinates in materials/ASTR210/reference-log.md.