Instruments

The Santa Barbara Instruments Group (SBIG) ST7E camera is designed especially for amateur astronomers to take images with small telescopes. It has a Kodak KAF-0401E charged coupled device (CCD) detector with $765\times510$ pixels, each $9\mu m$ square. (A $\mu m$ or micron is 0.001 mm.) The detector is sensitive from the near ultraviolet around 350 nm to the infrared around 1100 nm (or 1.1 $\mu m$). Typically the detector is operated well below room temperature in order to reduce the thermal dark signal. With the electronics that interface this sensor to the computer, one digital unit (so-called analog-to-digital unit or ADU) corresponds to 2.3 electrons in the sensor. Each incident photon that is detected creates a photoelectron, and the probability of a single photon being detected is about 65% at the maximum of the quantum efficiency curve. At $0~C$ there will be about 1 electron per pixel per second due to the thermal dark current, that is, electrons which are freed from their potential well by their own kinetic energy rather than by the energy of the incident photon.

The detector is at the focus of a small spectrograph which forms an image of a spectrum on the CCD. The signal from each pixel of the CCD is proportional to the number of photons that fall at that point during the exposure. Different positions along the CCD correspond to different wavelengths of light, so the image you will see reveals the spectrum of the light source dispersed across the detector.

The Acton Research 300i spectrograph covers from 180 to 1400 nm, resolves 0.1 nm, and sets to a selected wavelength to within $\pm$0.2 nm. It is a Czerny-Turner design with two f/4 aspheric mirrors, one to collimate the light that strikes the grating, and the other to focus the spectrum. By making the mirrors aspheric (not spherical) and by a design that optimizes where the mirrors and the grating are located, it is possible to have very good focus and image quality across the flat surface of the CCD. There are three gratings in a turret that is rotated by a stepping motor. The selection of grating and wavelength is controlled by this motor using simple commands to the computer in the spectrograph.

Each pixel of the CCD covers $9\mu m$ in the focal plane of the spectrograph. The spectrograph disperses light across the focal plane with $d\lambda/dx$ (nm/mm) as shown in the table below, and accordingly each $9\mu m$ pixel covers $d\lambda$ (nm). Since there are 765 pixels across the width of the CCD, this scale determines how much of the spectrum is recorded in a single exposure. The table shows that to record detail it is best to use a finely grooved grating, but to record as much of the spectrum as possible it is better to use fewer grooves/mm. Also, with detector elements $9\mu m$ across, and the entrance slit imaged at each wavelength on the detector, the instrument will have its best resolution when the slit is set at $9\mu m$ as well.

Diffraction Gratings
ID	Grooves	Blaze $\lambda$	$d\lambda/dx$	$d\lambda$	Coverage
	$\mathrm{mm}^{-1}$	nm	nm/mm	nm/pixel	nm
1	2400	240	1.389	0.0125	9.56
2	1200	500	2.778	0.0250	19.1
3	300	1000	11.11	0.0999	76.4