Methodology

The absolute calibration of the reference standards-detectors used for ACIS quantum efficiency measurements-was performed using the Physikalisch-Technische Bundesanstalt (PTB) laboratory in the BESSY electron storage ring. Undispersed synchrotron radiation was used as the primary flux standard. Using the XSPEC fitting routine, a response matrix, constrained by spectral response measurements at MIT, was convolved with the known incident spectrum. The CCD gate structure parameters were then adjusted to minimize the $\chi ^{2}$ measure of fit. The quality of the resulting quantum efficiency model hinges on the accuracy of our knowing the synchrotron radiation. The spectral flux can be calculated with relative errors below 1% from the physical geometry of the detector with respect to the orbital plane of the electrons and other storage ring parameters: electron energy, ring current and magnetic field of the bending magnets  [Arnold and Ulm1992].

Figure 4.57 illustrates the experimental set-up at the PTB laboratory. A standard MIT vacuum chamber, modified to hold two CCDs simultaneously was mounted to the PTB beamline via a ceramic electro-isolator to eliminate electrical interference between the CCD electronics and the BESSY facility. A gate valve and turbo pump located between the CCDs and the storage ring allowed the chamber to be connected and pumped down to the requisite vacuum without compromising the integrity of the storage ring. The CCDs were operated at the nominal flight temperature of -120 C$\hbox{$^\circ$ }$.
 
 

Figure 4.57: Sketch of the PTB laboratory

Even with just a single electron in the storage ring, the incident photon flux would have caused significant pileup (defined as multiple photons landing in the same pixel or neighboring pixels during one integration time) in the CCDs and corrupted the absolute calibration. Two measures were taken to reduce the flux to an acceptable level. First, a chopper wheel with a 2.00% transmission cycle was inserted into the beam line to reduce the incident flux. Second, only 256 rows of the CCD were read out. This readout mode reduced the integration time by a factor of four. The storage ring was usually operated with currents between 10 and 30 electrons, although measurements with as few as 5 electrons and as many as 50 electrons were performed to determine pileup effects.

The process of reading out 256 rows of the CCD limited the amount of the detector that could be calibrated during one measurement. To ensure that all the incident photons would fall on an active area of the detector (a necessary requirement for the determination of absolute quantum efficiency) a five mm high aperture was placed in the beam line and carefully centered on the electron orbital plane. The five mm slit produced an illumination pattern 208 pixels tall, and the CCD columns were nominally aligned perpendicular to the orbital plane. A two dimensional translation stage was incorporated into the section of the PTB beamline that the MIT chamber mounted to. To calibrate an entire chip, the chamber was moved an appropriate distance in the y direction, a 256-row swath of the CCD was read out, and the image was visually inspected to check that all the photons hit the active area. This procedure was repeated four or five times to calibrate the entire chip. The chamber was then moved in the horizontal direction to illuminate a second CCD inside the chamber. By placing two chips inside the chamber, the overhead associated with thermally cycling the CCD, venting the chamber, switching CCDs, re-evacuating the chamber and finally cooling the CCDs was eliminated. This configuration allowed calibration of as many as four chips in a single 48 hour user shift.

Given a well located electron beam, the synchrotron radiation from a storage ring can be derived from Schwinger's equation [Riehle and Wende1986,Schwinger1949]:

$${E(\lambda)^{SR} = E^{SR, \Vert}(\lambda) + E^{SR, \bot}(\lambda) =}$$

$$\frac{2e\rho^{2} I}{3 \varepsilon_{0} \lambda^{4} \gamma^{4} a d^......^{2}]^{2} (\gamma \psi)^{2}K^{2}_{\frac{1}{3}} (\xi) d\psi\end{array} \right\}$$ (4.25)

with

$$\gamma = \frac{W}{m_{0}c^{2}}, \ \ \ \ \ \ \xi = \frac{2 \pi}...... \frac{W}{ecB}, \ \ \ \ \ \ \psi^{\prime} = \frac {a}{2d^{SR}}$$

W, e and m₀ are the energy, charge and rest mass of the electrons and I is the current of the electrons in the storage ring. B is the magnetic induction of the bending magnets tangent to the observation point. a is the measure of the height of the beam, d^SR is the distance from the beam to the observation point, and $\psi$ is the opening angle between the orbital plane and the observation point. c and $\varepsilon_{0}$ are fundamental constants, and K_x is the modified Bessel function, order x, of the the second kind. Thus, the spectral photon flux can be expressed in terms of seven measurable quantities:

$$\Phi_{E} = \Phi_{E} (E; W,B,I,\Sigma_{y},d^{SR},a, \psi)$$ (4.26)

where $\Sigma_{y}$ characterizes the vertical position and divergence of the electrons at the observation point and the other quantities are the same as above. W and B were measured once for each run, and I was monitored continually. Horizontal variation of $\Phi_{E}$ is less than 10^-3 over the width of the CCD [Riehle and Wende1986]. Due to its dependence on the opening angle $\psi$,$\Phi_{E}$ varies strongly as the observation point moves out of the orbital plane of the electrons. Figure 4.58 shows how the BESSY spectrum softens as the height above the orbital plane increases. The calculated $\Phi_{E}$ is for one electron in the storage ring with no chopper wheel. For typical integration times and ring currents, no flux above 4 keV was detected by the CCDs.

Similar measurements were also performed using the PTB Wavelength Shifter (WLS) beamline. Additional magnets are introduced into the normal storage ring configuration, thus boosting the energy of the electrons and shifting the energy of the synchrotron radiation. Figure 4.58 also shows how the WLS spectrum changes as a function of height above the orbital plane. Although the spectrum extends beyond 20 keV, the low high energy quantum efficiency of the devices limits the detection of photons to below 14 keV. The WLS experiments will be discussed in greater detail in Section 4.6.1.3.
 

Figure 4.58:  White Light and WLS BESSY spectra as a function of height above the orbital plane.