As in any classic absorption experiment, our apparatus consists of three main components: a sample of absorbing atoms or ions, a continuum source, and a detection system.
An iron HCD provides a gas phase sample of 
distributed through
a large number of metastable levels. The cathode is water-cooled, 1 cm in
inner diameter and 10 cm long. The discharge uses 2.4 Torr of Ar as a buffer
gas; currents ranging from 250 mA to 1.2 A are used in this experiment.
Our continuum source is the white light beam line on the Aladdin Storage
Ring at the Synchrotron Radiation Center. The ring has a 2.083 m magnetic
bending radius and usually operates with an 800 MeV beam and 200 mA of
current. The continuum is both spectrally smooth and very stable and
covers the entire VUV range.
We have two separate spectrometer/detector systems since we measure relative f-values. One measures the ``reference" line; the other measures the ``unknown" line. By measuring both lines simultaneously, we eliminate the need for long term stability in our discharge.
One of the spectrometer/detector systems is an Acton Research
Corporation model VM-510, 1 m focal length vacuum compatible
spectrometer with a Princeton Instruments 15.5 bit 1024 element photo-diode
array (PDA). The spectral resolving power of this system is around 
, limited by the 0.025 mm spacing of the diodes in the array. This
system is used to measure a well isolated ``reference" line in the UV, so a
moderate resolving power is acceptable. The combination of the moderate
resolving power and high throughput of this reference spectrometer makes
it possible to use a PDA instead of a more sensitive CCD array. The
second spectrometer/detector system is a 3 m focal length vacuum
compatible echelle spectrometer equipped with a VUV-sensitive CCD detector
array. The practical resolving power of this system when used with the
256 mm wide, 
blaze echelle grating is 
. The CCD
is a Scientific Imaging Technologies uncoated, boron-doped, thinned,
back-illuminated, deep UV sensitive device in a camera head from Princeton
Instruments. The CCD format is square, 512 pixels on a side. Because the
spectrometer operates in 22nd to 36th order for these measurements, a
McPherson model 234/303 Seya monochromator is used as an order-sorter. To
reduce stray light in the spectrometer, we limit the Seya bandpass to 0.1
nm. This high resolution system is used to measure the ``unknown" line.
Figures 1 (click here) and 2 (click here) show sample UV spectra taken on the
low resolution and high resolution systems, respectively. The noise in the
continuum of each figure is consistent with Poisson statistics.
Figure 3 (click here) demonstrates the good signal-to-noise ratios of our high
resolution spectra in the VUV wavelength range.
Figure 1: Spectrum at 234 nm taken with the 1 m spectrometer
and PDA. The noise in the continuum is consistent with Poisson
statistics
Figure 2: Spectrum at 234 nm taken with the 3 m echelle grating spectrometer
and CCD array. The noise in the continuum is consistent with Poisson
statistics. The weak Fe II absorption line at 234.396 nm is completely resolved
and is observed with a good signal-to-noise ratio in this spectrum; the line is
barely visible in Fig. 1
Figure 3: Sample absorption spectrum of the 160.845 nm transition in Fe II. The
noise in the continuum is consistent with the Poisson statistics of the
photo-electrons in the CCD array
Our experiment is now sensitive to fractional
absorptions of 0.0003 using the 1 m spectrometer and PDA and is sensitive
to fractional absorptions of 0.003 using the 3 m echelle spectrometer and
CCD array. It has been possible to achieve sensitivities to fractional
absorptions of 0.00001 with modest spectral resolving powers
(Menningen et al. 1995). We are optimistic that the
experiment described here will ultimately achieve sensitivities to
fractional absorptions of 0.0001 with a spectral limit of resolution of
at wavelengths down to Lyman alpha. This goal corresponds to
measuring equivalent widths as small as 
or ionic
column densities of 
. A sensitivity in this range will
extend the dynamic range of the f-value program, and will make our
absorption experiment a more powerful plasma diagnostic than a typical
laser induced fluorescence experiment on a glow discharge. This sensitivity
goal is likely achievable through a combination of improved optics and
improved detector arrays. The use of a storage ring beam line with an
insertion device would also help.
We have carefully reshaped the synchrotron beam using several cylindrical mirrors to match the angular acceptance of each spectrometer; the optical coupling is described in detail elsewhere (Bergeson et al. 1996b). The etendue of the reshaped synchrotron beam is a rather good match to the etendue of the 3 m echelle spectrometer. The synchrotron beam does not have a large enough etendue to a fill a typical Fourier Transform Spectrometer (FTS). The lack of a useable etendue advantage, along with a signal-to-noise disadvantage from the spectral redistribution of quantum (Poisson) noise intrinsic to an FTS, means that an FTS does not have an advantage over a grating spectrometer in this experiment.
We use a digital subtraction technique to discriminate against line emission in the HCD (Wamsley et al. 1993). With the synchrotron continuum passing through our sample, the spectrum is a combination of the synchrotron continuum, absorption from atoms and ions in the line of sight, emission from the HCD and dark signal from the array. By blocking the synchrotron, we get a spectrum of only the HCD emission plus the dark signal. The subtraction of these two spectra results in the continuum plus absorption spectrum. Pixel to pixel variations in the quantum efficiency of the detector can be accounted for by dividing the difference spectrum described above by a dark signal corrected, high signal-to-noise continuum spectrum taken with the HCD off.
When using this digital subtraction technique, the linearity of the detector arrays is especially important (Menningen et al. 1995). We measure the fractional non-linearity of our CCD array and find it to be less than 0.001 from 4% full well to 85% full well. We have designed our optical coupling so that the HCD line emission is much less than the synchrotron continuum. In this situation, the small non-linearities of the detector have no effect on our absorption signal.
Precise temporal gating of the detector arrays is also essential for reliable digital subtraction of the HCD line emission spectrum. The standard readout procedure of a CCD array involves shifting the photoelectron pattern across the array. This procedure may not provide the required precision gating. Wamsley et al. (1993) used a gated image intensifier to achieve the required precision. Image intensifiers have many disadvantages in a high sensitivity absorption experiment. They are expensive and easily damaged. They also reduce the saturation fluence of the array, decrease the spectral resolving power of the experiment, and add noise to the spectra. A frame transfer technique, in which the photoelectron pattern from the exposed part of the CCD array is rapidly transferred to a masked part of the array, provides precise gating of the CCD array. The normal readout mechanism of the PDA provides precise temporal gating.
Scattered light can cause an error in absorption measurements; we have taken special care to accurately account for any scattered light in our system. Earlier tests have verified that the scattered light level in this experiment is less than 1% of the continuum (Bergeson et al. 1996b). A small correction eliminates any error due to scattered or ``leakage" light.
We see evidence of a non-Maxwellian velocity distribution in our
discharge. A model of our discharge suggests that this is due to competition
between the ambipolar diffusion (ion loss) rate and the collisional
thermalization that fills out the high energy tail of the Maxwellian profile.
With our discharge parameters and operating conditions, the diffusive loss rate
and collisional thermalization rates are nearly the same. Thus the more
energetic ions diffuse out of the negative glow to the cathode of the discharge
and are thus lost at a higher rate than low energy ions. Collisional
thermalization is unable to completely ``fill out" the high energy tail of the
Maxwellian distribution. This is referred to as ``diffusive cooling" and results
in a truncated Voigt profile. While operating with a resolving power of
, we are unable to resolve the lineshape of an absorption
feature. We have experimented with a variety of approximations for
generating a curve of growth. The simplest and most satisfactory
approximation is to use a full Voigt profile in our curve of growth
analysis with the Lorentzian component being primarily radiative
(natural) broadening. To determine an ``effective" ion temperature of
our discharge, we measure several strong UV line pairs with well-known
f-values at a given discharge current and find the temperature which
gives the best overall consistency for all of the f-value ratios.
Since we continue to assume a full Voigt profile in our curve of growth,
the result of our temperature determination is artificially low or
unphysical (below 293 K, the temperature of the HCD cooling water) for
discharge operating currents below 300 mA. We recognize that this
effective ion temperature is not a true heavy particle temperature of the
discharge, but we use it in analyzing 
absorption data with
the discharge operating under a well defined set of conditions. This
effective ion temperature is used to determine the curve of growth for
all other data taken under the same discharge conditions. Table 1 shows
the effective ion temperatures and the resulting absorption f-value
ratios for several pairs of lines sharing a common lower level at each
HCD current setting used in the experiment. A few entries are missing in
the bottom row of Table 1. The largest f-value ratio was not measured
at the highest currents because the highest currents were used only for
measuring the weaker lines. The solid agreement between the absorption
data from this experiment and the accepted f-value ratios from
emission branching fraction and laser induced fluorescence lifetime
measurements reported in the literature demonstrates the reliability of
this method over a wide range of discharge conditions.
Table 1: Well-known absorption f-value
ratios for pairs of lines sharing a common
lower level in Fe II and our measurements at
each hollow cathode discharge current used in
the experiment. The last row gives the
effective ion temperature used for the Voigt
profile in the curve of growth analysis. The
number in parentheses following a table entry
is an uncertainty in the last digit(s) of the
table entry