Figure 1 - Spectra of HD44179 and its associated nebulosity. Heavy line, the nebular spectrum of HD44179. Thin line, low resolution spectrum of HD44179, scaled down by a factor of ~1300 to fascilitate comparison with the nebular spectrum.
Affectionately termed the Red Rectangle, the nebulosity associated with the bright star HD44179 exhibits an extended emission in the red region of the visible spectrum. The star system is throwing off two conical jets in opposite directions, producing an X-shaped pattern of gas.1 Optical spectrophotometry of the nebula has revealed narrow emission lines, but the overall feature, which strongly resembles the emission spectra of some molecules, remains unidentified.2 Furthermore, astronomers have surmised that a ring of matter surrounding this star system may be a site of planet formation.1 The goal of this research is to generate a representation of the extended emission so that it may be better characterized. By digitally removing the central star from an image of the nebula and star, a semblance of the extended emission will remain.
This study examines images of the nebulosity at three specific wavelengths. A procedure was developed to generate a point spread function of the central star in an image taken at a wavelength in which no extended emission is exhibited. This function is then subtracted from images of the Red Rectangle at two distinct wavelengths, both of which correspond to the most prominent unidentified features in the nebula’s spectrum. An obstacle to the successful removal of the central star is the degree to which the point spread function can be scaled and shifted to match the peak intensity in subsequent images.
Previous efforts in generating a representation of the extended emission were unsuccessful.3 Images were tainted by using an interference filter which was not completely normal to the incident light thereby producing ghost images. This attempt has made use of a tunable liquid crystal filter for spectrophotometric observations. Initially, our aim was in characterizing the properties of a tunable liquid crystal filter for astronomical study. While the focus of this research drifted toward image processing over the course of the year, the utility of this device was invaluable in obtaining the necessary imagery, and its properties will be put to continued use in the future.
The Red Rectangle
HD44179 is a bright B9-A0 III star with an associated biconical nebulosity.2 The star system, roughly 1,200 light-years from Earth, is throwing off two conical jets in opposite directions, producing an X-shaped form.1 Spectral characteristics of this nebulosity have long puzzled astronomers. From Figure 1, optical spectroscopy of the nebula reveals a broad emission bump superimposed on the stellar spectrum.2 Strong emission lines within this region are yet unidentified (Table 1). Furthermore, recent detection of a ring of matter around the Red Rectangle has created speculation that this nebula may be a sight of planet formation.1
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Similar research was previously conducted, however the results proved inconclusive.3 In that research, images of the Red Rectangle were compared in order to detect any differences in the nebula’s appearance between H-alpha and a nearby red emission line. Narrow-band interference filters were used to image the nebula at 540 and 690 nm while a broadband filter was used to image the nebula over the entire visible spectrum. It was determined that an oversight occurred the instrumentation, tainting the data used.3
Interference filters were used in the acquisition of multiple direct images of the same field. These fixed-bandpass interference filters record light in a band region containing spectral features of interest, blocking shorter and longer wavelengths while transmitting a band in between.4 This technique possesses several drawbacks. Certain band-pass filters will transmit in either the visible or near infrared, ie leak, hence care must be taken. Ambient temperature and angle of incidence will also affect their performance5. In addition, using multiple filters creates difficulties in handling, due to the shear number needed for multispectral imaging.
This research demonstrates the usefulness of a new approach to multispectral
imaging in astronomy. The technique utilizes a tunable, liquid crystal
filter in front of a CCD camera to produce spectrophotometric images of
the emission nebula.
With the use of a tunable liquid crystal filter, the Red Rectangle can be easily imaged across the visible spectrum. This approach combines the best features of filter imaging (complete spatial coverage) and conventional spectroscopy.6 A tunable, liquid crystal filter is essentially an optical filter that is able to select a particular center wavelength for transmission and reject wavelengths outside this band. The structure relies on constructive and destructive interference effects in a multi-layer stack of quarter-wave reflective layers and half-wave spacer layers. This serves to introduce phase delays between the two orthogonal polarized components of the electromagnetic wave, or provide retardance.7
As shown schematically in Figure 2, each cell consists of an initial linear polarizer, followed by a birefringent element (material that displays two different indices of refraction) of fixed retardance, then the variable retarder consisting of a liquid-crystal waveplate, and a final analyzer oriented with its axis parallel to the initial polarizer.7
Figure 2 - Schematic representation of a tunable liquid crystal filter
cell7
Intrinsic to the LCTF is an added liquid crystal waveplate at each stage providing an electronically controllable variable retardance. The liquid-crystal waveplate consists of two transparent electrodes, coated with indium-tin oxide, on either side of a cell containing nematic liquid crystals.7
The LCTF used here is a Cambridge Research & Instrumentation, Inc. Varispec filter model #VIS2-1012. The filter has a fixed spectral bandwidth of 10 nm, with a central wavelength electronically tunable to any wavelength between 400 and 720 nm. The filter transmission is sensitive to the degree of polarization of the input beam. Transmittance varies from 31% at the red end (720 nm) to 5% at 435 nm for randomly polarized incident light.8
The LCTF has a 35mm circular clear aperture and a field of view of +/-
7 degrees from normal. The filter is a high-contrast version with
less than 0.01% average out-of-band transmission. The response time
of the filter for altering wavelengths is 50 ms at 25°C.8
Spectrophotometry is the accurate measurement of the flux emitted by an astronomical object as a function of wavelength.4 Spectrophotometry of emission lines is the principle tool for studying the compositions of star and gaseous nebulae.6 In studying extended sources, such as emission nebulae, we are interested in obtaining spectra of a number of regions so that we can identify changes in the nebula as a function of wavelength.
The intrinsic flux distribution of the object is affected by many factors during propagation through space. Two such factors of importance are the passage of the light through the atmosphere, and its collection by the telescope and CCD camera.4 The atmosphere blurs our data beyond that expected from the diffraction limit of the telescope. This blurring should be constant however between our exposures.
A basic procedure for obtaining photometric data from CCD images is profile fitting, also called point-spread-function (PSF) fitting. Here, the PSF is the actual recorded profile on the detector of an unresolved, point source. This method relies on fitting the image recorded. Mathematical curves are “fitted” to the real data using computer programs until a good match is obtained.
The image of the central star of the red rectangle is compared to a Gaussian intensity profile of the form:
measures
the width of the distribution. It is often convenient to describe
the PSF in terms of its full width at half of the maximum intensity; the
FWHM (in pixels) is related to 
by equation 1
Various programs are available for photometric analysis including the DAOPHOT package included in IRAF (NOAO/Tucson). Such programs will locate the centers of bright stars, and fit an appropriate profile. This profile can be subtracted away to reveal fainter stars in the field, or in this case, nebulosity.
The use of CCDs for photometric measurements is founded on two basic assumptions9, namely,
(1) the response of each pixel is a well-defined function of exposure
level, optical
bandpass, and device architecture control. Considerable
effort is required to fully
optimize and stabilize detector performance for precision photometry.
(2) the incident signal from the astronomical source can be calibrated.
It is also assumed that when the basic CCD calibration procedures of bias subtraction, dark subtraction, and flat fielding have been applied correctly, that these effects are small.
The basic principle of psf photometry is that all images on an individual
CCD fame have, again baring any distortions introduced by optics, the same
form and thus differ from one another only by a scaling ratio.10
The procedures implemented in this study are founded on this principle.
In addition, we seek to extend the premise to say the profile is unchanged
between successive CCD frames. The goodness of the match between
point spread functions on varying frames will be an indication of the degree
of accuracy to which we can claim.
Image Acquisition
In October of 1997, Elliot Horch acquired images of the Red Rectangle at the University of Toronto Southern Observatory 60 cm telescope at Las Campanas, Chile using a front-illuminated Kodak KAF-4200 CCD set inside a Photometrics CH-250 camera head operating at approximately –50 ?°C. Two images were selected for comparison. One was exposed for 800 seconds with the filter’s central wavelength set to 525 nm (Image 1) and the other was exposed for 400 seconds at 638 nm (Image 2).11 At 525 nm, we believe the image is representative of the central star of the nebula. This will serve as the model for which we will build a point spread function of the central star. At 638 nm, an extended emission is observed.
Images of the Red Rectangle were recorded in FITS format (Flexible Image Transport System). This system is the recognized standard format for image files among professional astronomers developed by Don Wells, Eric Greisen, and Ron Harten.9
| Image #1 | Image #2 |
Image Reduction Analysis Facility (IRAF)
The IRAF facility is used for all image processing in this study.
IRAF is a product of the National Optical Astronomy Observatories (NOAO)
and provides a range of image processing tools using a command line interface.12
Application programs, called tasks, are arranged into a hierarchy of packages
of related functionality. The IRAF package CCDPROC was used for the
reduction of data. DAOPHOT, a large program developed by Peter Stetson
of the Dominion Astrophysical Observatory in Canada, was utilized for the
majority of photometric analysis.9
The tasks DAOFIND, PHOT, PSF, and ALLSTAR are included in this program,
and are the primary analysis tools utilized in this study.
Data Reduction
Before any photometric analysis can begin, the data must be reduced. A reduction process is a series of steps taken to decrease the influence of imperfections inherent in the CCD camera on the estimation of a desired quantity, or to reduce noise sources.13 Such noise sources were removed from our object images through a sequence of reduction steps. These steps included overscan trimming, subtraction of bias, and division by a flat field. No hot pixels were detected in analyzing the available dark frames, therefore dark subtraction was not necessary, and would have only added noise. Cosmic rays have not been removed.
First, the overscan data of an image must be removed. Overscan data is acquired by continuing to readout a line of the CCD past its physical extent.13 This is a common practice in CCD astronomy. After subtraction of the overscan level, the noise level on any remaining count level must be (at least) Poisson.13
Similarly, a bias frame was subtracted from each raw CCD image. It is likely that the electronics involved in the CCD camera will have an inherent pattern that is associated with each readout. This noise can be thought of as viewing with no signal.13 Such a two-dimensional background is referred to as bias. A removal of this additive factor is essential for reduction.
Finally, the images were flat fielded using an image of a uniform illumination.
Different pixels of the CCD have different quantum efficiencies (percentage
of the incoming light that is converted to electrical charge) resulting
from structural variations in the CCD itself.9
Flat fielding corrects for such pixel to pixel gain variations. Since
the quantum efficiency variations of the CCD pixels have a dependence on
wavelength, dome flats were taken over the range of wavelength settings
of the filter. The flat field image used was that closest in wavelength
to that of the object frame.13
Locating Peak Intensities
DAOFIND searches an image for local density maxima, with a full-width
half-maxima specified in the data parameter file, and peak intensities
greater than a threshold value by a specified number of sigma, and then
writes a list of detected stellar objects to a coordinates file.
The task also calculates X and Y centers of the objects by estimating the
x and y positions of the best fitting one-dimensional Gaussian functions
in x and y respectively.12
These coordinates are also included in the output file and listed to a
thousandth of a pixel.
Scale Factor Determination -
In order to match a point-spread function to varying CCD frames, the brightness os individual stars must be obtained. PHOT computes background sky values and magnitudes for the objects in the specified coordinate file. By default, the task will not recenter the star because the DAOFIND task has already computed accurate centers.12 Input to the task is the coordinate file (output from DAOFIND) and an aperture of a specified radius of 30 pixels. From this, PHOT generates an areaof the aperture, sum total of counts within the aperture, and sky value msky (using a mode algorithm), and subsequently computes the total flux (equation 2).12
flux = sum - area * msky (2)
The magnitude of the star will not be accurately computed here due to a lack of information in the image header that is required by the PHOT task.
From the calculated flux in both images, a scale factor between the
two images can be determined.
Point Spread Function Fitting
.
The PSF task builds a point-spread function of specified radius for
stars specified in the photometry file (output by PHOT). In fitting
a point spread function to the intended star, the task requires a fitting
radius be specified which is the approximate FWHM of the star. Only
pixels within the good data range are included in the fit. The output
file containing the computed point spread function is a two-dimensional
“image” carrying the analytic component of the psf and header information
for center position, magnitude, and size. A look-up table of residuals
from the fit is created separately. The analytic function fits the
light distribution in the core of the star with a Gaussian model.
Residuals are stored as a look-up table with twice the sampling interval
of the original image. This look-up table is used as additive corrections
from the analytic function to the actual empirical psf. The brightness
of any pixel is computed by integrating the function over the area of the
pixel. A correction is determined by bicubic interpolation within
the look-up table and added to the integral.12
Profile Subtraction
The ALLSTAR task is used for profile subtraction. ALLSTAR subtracts
a given psf image (output of PSF) from stars at x and y locations given
in the photometry file (output of PHOT). The task produces a two-dimensional
output image, giving the number of iterations it took to fit the point
spread function and a goodness of fit statistic chi which is the ratio
of the observed pixel-to-pixel scatter in the psf fitting residuals to
the expected scatter. ALLSTAR recalculates the x and y centroids
of the star. The star is rejected if the centroids differ by more
than 0.002 pixels from one iteration to the next.12
Data Reduction
The section of the CCD frames [2:2032, 2:2044] in x and y respectively is found to contain the image. Consequently, the remaining section [2034:2038, 2:2044] is considered the overscan section of the area, and is trimmed from the image. A bias frame was constructed from the median of several exposures taken with the shutter to the CCD camera closed. This median was then subtracted from each subsequent data frame. A mean flat-field frame was created for each image by averaging several independent exposures at the same wavelength. The process was completed with the division of the flat field frame into the object frame.
Coordinate files containing the location of the peak intensity of the Red Rectangle are generated for Image 1 and 2. The DAOFIND task is run on both images in order to obtain a list of objects in the frame. The threshold sigma is raised until the coordinat list generated contains no more than a few locations. Using a basic text editor, all objects except for the Red Rectangle are removed from the coordinate file. These coordinates correspond to the peak intensity location of the nebula, and will be utilized in subsequent tasks for photometry and psf fitting.
Upon finding the centroid coordinates of the Red Rectangle in Images
1 and 2 with DAOFIND, the flux at both locations is determined. Input
to the task is the coordinate file (output from DAOFIND) and an aperture
with a fixed radius of 30 pixels. From the calculated flux of both
images, a scale factor between the two can be determined (Table 2).
Image 1 is then scaled up to match the peak intensity of that found for
Image 2.
|
|
|
|
|
|
|
|
525 nm |
|
|
|
|
|
|
638 nm |
|
|
|
|
|
|
525 nm |
|
|
|
|
|
A profile is generated for the Red Rectangle in Image 1 using the PSF
task. In fitting a point spread function to the intended star, a
fitting radius of 10 pixels is used. This is the approximate FWHM
of the star. Only pixels with values in the good data range -100
to 15000 are included in the fit. The point spread function generated
can be seen in Figure 3. This will serve as the model of the central
star of the Red Rectangle.
Figure #3 - Point Spread Function Calculated for the Red Rectangle Image Acquired at 525nm
Before an attempt is made to produce an image of the extended emission present at 638 nm, the point spread function is put to two tests. It is important to verify that the profile accurately fits the central star before any analysis can be made on additional frames. First, the form of the generated profile is checked for accuracy by subtracting it from the peak location of the Red Rectangle in Image 1. In essence, it is subtracted from the object used to generate it. Figure 4 is the resulting intensity distribution for this location. As seen in the line plot across the image, the nebula has been virtually cancelled out.
Second, the ability to scale the point-spread function to match an alternate
peak intensity is checked. The psf (appropriately scaled) is subtracted
from Image 1 at a location corresponding to an additional faint star in
the same field. Since objects on the same CCD fame have, again baring
any distortions introduced by the optics, the same form, the profile of
the two should differ only by a scaling ratio. The coordinates and
photometry for this smaller star are calculated using the same procedure
determined for the Red Rectangle. Image 1 is scaled down to match
the peak intensity of the faint star (Table 2), and a psf is fit to the
Red Rectangle. Figure 5 shows the result of subtraction of the scaled
point spread function from the faint star in Image 1.
|
|
|
Finally, the procedure is applied to an image of the Red Rectangle at a wavelength in which an emission line is known to be present in the nebula’s spectra. An image acquired at 638 nm (Image 2) was chosen for this purpose. After application of the calculated scale factor to Image 1, a point spread function is generated for the Red Rectangle. Image #3 shows the result of subtraction of the point spread function, scaled by the appropriate factor (see Table 2), from the Red Rectangle in Image 2. A contour plot of the original image at 638 nm (Image 2) can be seen in Figure 6, and is clearly dominated by the presence of the central star. In contrast, Figure 7 represents a contour plot of the reconstructed image. There are five contour levels in each plot of the nebula. Dashed contours indicate a negative value. A positive “peak” with a surrounding negative "well" seems to have been left at the center of the nebulosity.
Image #3
|
|
Figure 7- Contour Plot of Image 3 |
The complete removal of the point-spread function from the image of the Red Rectangle at 525 nm indicates that the fitted profile modeled the central star of the nebula well. Since the psf is merely a mathematical fit to the data, and not an exact representation, Poisson deviation at any point in the profile is present. Psf removal from the faint star at 525 nm, on the other hand, results in a residual intensity distribution. This distribution exhibits a peak intensity with a surrounding negative lobe. This result indicates that the profile was too low at its peak and too broad. Nebulosity present in the Red Rectangle at 525 nm would produce such a profile. Although no extended emission has been reported at this wavelength, the broad psf suggests that there may be a slight nebuloscity associated with the star in this frame.
Subsequently, if this model is not suitable for object subtraction within the same frame, it will not be adequate for generating a representation of the extended emission at other wavelengths of interest. The constructed representation of the extended emission at 638 nm resulted in a marked negative then positive “shadow”. This effect echoes the result seen in the psf removal from the frame taken at 525 nm. The profile is too shallow at the peak and too broad to accurately remove the central. The contour plot of the reconstructed image of the nebula reveals a rectangular-shaped structure around the central location of the nebula. This form is the characteristic emission shape which has given rise to the nebula’s enduring name, and is an encouraging result.
Registration errors may also exist. This is more difficult to verify due to the lack of fit of the profile function, however, the direction and magnitude of the negative dip would indicate a possible direction of overshifting. If the peak intensities are not aligned properly it is very likely that the centroids of the images were not computed with enough precision. To test this assertion, the point-spread function could be manually shifted by small fractions of a pixel. Any changes in the intensity distribution of the reconstructed image would be telling as to the degree of alignment of the point spread function.
In the future, we will endeavor to hone the fitting procedure.
An average . Since the field of view over the frame is so small,
the optical transfer function can be considered constant. Subsequently,
creating an average profile using several stars in the field would be plausible,
and is being considered. The locating of stellar centroids is also
under verification. In addition to the images presented here, other
wavelengths of interest are being examined. Emission lines at 582,
and 605 nm have been imaged and are to be fit with the model point spread
function. This may give further insight into the nature of any inaccuracies
in the profile.
While the task of removing a fit of the central star from images of the nebula has been completed, conclusive statements about the success of this methodology cannot be made until the accuracy of the centering of the psf with respect to the images in question is evaluated. Further testing of centering algorithms and accuracy of the point spread function determined is currently underway.
Profile fitting is far from an exact science. Many variables must
be taken into account when attempting to match varying frames with one
point spread function. It may be the case that there are too many
variables. Perhaps the atmosphere caused variation between the frames.
Perhaps the chosen function is simply not a good representation of the
actual image. Still, the procedure has merit, and shows an encouraging
beginning. Many avenues have been ruled out, and while the extended
emission could not fully be characterized here, the methods to profile
fitting have been explored and are of greater understanding.