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Lab #1: Photon counting & detectors
Lab report is due Sunday, February 2, 2025 by 11:59 pm PT
1 Introduction & Overview
This handout provides a description of the activities that we will explore in the first lab. Because we use this first lab to introduce many new skills, especially Python programming, this handout is a guide that your lab group should follow.
At X-ray, ultraviolet, optical and infrared wavelengths, most astronomical instruments employ the photoelectric effect to convert photons into electrons, which can then be counted and recorded. Since the 1930’s astronomers have used photomultiplier tubes, which employ the photoelectric effect in vacuum (Figure 1). Modern detectors are based on the solid-state devices constructed from semiconductor materials. In this lab we will investigate the properties of a Charged-coupled Device (CCD) integrated circuit that uses the photoelectric effect in silicon to record visible light.
Figure 1: Photoelectric effect: photons (on the left) strike a surface and electrons are liberated.
The process of photon detection and counting is not perfect—detectors have flaws that introduce noise and various systematic errors into the measurement process. The purpose of this lab is to explore the operation of a CCD optical sensor to learn how to generally characterize the properties of detectors. You will learn how to operate an astronomical CCD detector that is installed on the Nickel 1-m telescope at Lick
Observatory. Your team will use the instrumental software and controls, record images, operate the telescope, and use the Python programming environment to examine the digital data and learn about fundamental statistics of photon counting.
1.1 Schedule
This is a three-week lab with activities and lectures between January 7 and January 23. Your lab report is due on Sunday, February 2 via the submission link on Canvas by 11:59 pm. By the end week 1 your group should have completed key steps 1-3 (see §1.4). By the end week 2, groups should be prepared to discuss steps 4–6 during the “Group-Led Discussion”. By the end of week 3, groups should have progressed through steps 7-8 and have begun writing their lab reports. As you go through the lab exercises, remember to take notes, save figures, and document/put comments in your code so it will be easier to write-up your individual lab reports. Note that your written science report should not regurgitate this lab handout and should treat this experiment as if it Astronomy 150, Winter 2025 has been carried out as an independent research project. Do NOT copy text directly from this handout in your lab report.
1.2 Goals
Explore physical limitations on the detection of light. Investigate how precisely brightness can be specified, and what determines that precision. Explore optical imaging sensors and learn about detector noise and various systematic errors into the measurement process. Collect observations of dark and light frames with the Direct
Imaging Camera CCD on the 1-m Nickel telescope. Read the data into Python and examine the statistical properties of the data to measure detector gain and read noise.
1.3 Reading assignments
• Training with Python
o Work through the Python Notebook assigned as Coding exercise #1. You should learn how to use this powerful programming language to compute statistical quantities and make plots.
o References for important Python packages we will be using are:
§ Numerical computing: http://www.numpy.org/
§ Plotting: http://matplotlib.org/
• Review documentation for the Nickel 1-m telescope and Direct Imaging Camera
§ These pages describe how to operate the Nickel 1-m telescope: http://mthamilton.ucolick.org/techdocs/telescopes/Nickel/intro/
§ These pages describe the Direct Imaging Camera:
§ http://mthamilton.ucolick.org/techdocs/instruments/nickel_direct/intr
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1.4 Key steps
You will execute nine key steps in this lab:
1. Review the Nickel 1-m telescope and Direct Imaging Camera documentation on-line;
2. Take daytime engineering data sets on January 9 that include “bias frames” and “flat field frames” that follow this lab handout;
3. Read in FITS frames and plot 2D images with axis labels;
4. Plot histograms to visualize the statistical properties of different data sets with varying exposure times;
5. Compute the mean and standard deviation for your samples and investigate the variability of the count rate. Explore how the mean and standard deviation vary as the mean counts per frame increases;
6. Compare the observed histograms with the theoretical Poisson probability distribution function;
7. For data sets comprising multiple sequences compute the mean of the mean (MOM) and the standard deviation of the mean (SDOM). Show the MOM and the SDOM vary with the number of frames;
8. Examine the statistical properties of the data to measure camera gain and read noise;
9. Write your lab report.
2 Charge-Coupled Device (CCD)
We will use an image sensor based on a Charged-Coupled Device (CCD) integrated circuit. A CCD sensor is a two-dimensional array of pixels, each of which contains a photo sensitive area that is capable of measuring an electric charge that is proportional to the light intensity. Electrons are generated in each pixel by the photoelectric effect in proportion to the number of photons incident at that location. Each pixel accumulates charge and a control circuit then shuffles the photoelectrons down columns to a horizontal shift register, which in turn carries them to an amplifier where the charge is converted to a voltage. Each pixel’s voltage is sampled, converted to a digital signal using an analog-to-digital converter, and stored in memory to generate an image.
The digital signal is recorded in units known as analog to digital units (ADU). Assuming that the measuring circuits are linear, there is a linear relationship between ADU and the number of photoelectrons collected; this constant of proportionality is known as the gain. Each photodiode is reset at the end of an exposure by connecting it to a fixed voltage. This establishes a well-defined charge state at the start of the subsequent exposure.
The photo-charge, , is determined by measuring the voltage induced on a capacitor of capacitance, C, . (1)
This voltage is therefore directly proportional to the number of incident photons.
One of the principal goals of this lab is to measure the constant of proportionality in Eq. (1).
2.1 Types of detector noise
The above considerations imply various noise sources—both statistical and systematic—associated with the detection of light.
• Poisson noise—this is the fundamental noise associated with counting photons
(or photoelectrons). To a good approximation, photons follow Poisson statistics, so the standard deviation in an experiment that counts on average photoelectrons is .
• Bias – signal that is present even when there is no illumination and no exposure time (b). It can vary from pixel to pixel, and produces a systematic offset that must be subtracted to find the true level of illumination. Bias signals are typically added to CCDs on purpose so that the readout noise never drives the analog-to-digital input negative.
• Dark current—electron hole pairs are created by the photoelectric effect; they can also be created by thermal fluctuations (phonons in the crystal lattice) and quantum tunneling. This dark current produces a systematic error that, like bias, must be subtracted. Dark current also contributes Poisson noise because the
QPE
V = QPE C
NPE
NPEA
total number of charge carriers counted is increased to , where ND is the mean number of dark current electrons, and corresponding standard deviation is .
• Readnoise is the measurement error associated with determining the voltage represented in Eq. (1). For example, in an RC (Resistor-Capacitor) circuit, due to thermal fluctuations the rms voltage is . In Eq. (1) if C = 1 pF and T = 273
K then the rms charge, , introduces a measurement noise of 380 e- rms.
While there are ways to circumvent noise, e.g., by double correlated sampling, there is always some statistical error associated with measuring the voltage represented in Eq. (1). This error is typically called the read noise.
3 Nickel 1-meter Telescope and Direct Imaging Camera
We will be using the Nickel Telescope for this lab. The Nickel telescope is a generalpurpose, 40-inch (1-m) telescope used for astronomical imaging and spectroscopy. It is housed in a dome at the north end of the historical Lick Observatory building located on Mt. Hamilton, near San Jose, CA. The Nickel telescope can be used either by local observers or in a real-time, remote control observing mode. Our groups will be using the telescope and direct imaging camera from the UC San Diego Remote Observing Room (SERF 376).
The Direct Imaging Camera sits at the f/17 Cassegrain focus (behind the primary mirror) of the Nickel 1-m telescope. The camera is optically simple, consisting of an aperture wheel, filter wheel, and shutter, contained in an assembly in front of the focal-plane CCD detector, lying behind a fused-silica window in a liquid nitrogen dewar. The Direct Imaging Camera is equipped with a 2048 × 2048 pixel CCD array that is cooled to liquid nitrogen temperatures (77 K). Details of the facility are listed in Table 1.
Figure 1: A picture from inside the dome of the 40-inch on Mt. Hamilton. (Photo: Bill Keel, U. Alabama)
NPE + ND
NPE + ND
kT C
kT C
kT CAstronomy 150, Winter 2025
Lab #1
@2025 UCSD Astronomy 150
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Table 1: Nominal observatory and instrument properties
Site
Mt. Hamilton, CA
Geographic location 37°20’49”N 121°37’48”W
Primary mirror
1-m (diameter)
F/ratio-focal length
F/17 – 16,840 mm
Camera
CCD-2 (aka Dewar#2)
Detector
LN2 cooled Loral CCD
CCD format
2048 × 2048, 15.0 μm pixels
Nominal pixel scale 0.184 arc seconds/pixel (unbinned)
Field-of-view
6.3 arc minutes (square)
Optical Filters
UBVRI
Limiting Magnitude
R ≈ 17.5/18.5 mag. (10/60 seconds)
3.1 Controlling the Nickel and Direct Imaging Camera
The Lick Observatory websites (Section 1.3) outline in detail the control of both the
Nickel telescope and instrument. Each group will be using these websites in real-time while taking observations. There are multiple GUI (graphical user interfaces) that control both the telescope, dome, calibration lights, and direct imaging camera. We recommend that each group takes detailed notes during their observations so they can properly report back their experiment.
For the telescope and dome you will make use telescope control graphical user interfaces (GUIs). Note that there are safety buttons in the GUI to ensure the safety of the equipment before you can move the telescope or the dome. Nickel POCO (short for POinting and COntrol) provides control of the Lick 1-meter Nickel telescope and dome. The POCO interface has the top-level functions and displays for the telescope and dome.
Telescope POCO Functions