A quick list of the basic
techniques of x-ray analysis:
look at an x-ray image
using ds9 to get a qualitative feel for the data
use ds9 to select one or
more regions of interest
perform quantitative analysis
- spatial, spectral, or timing analysis - on the regions you
have selected
In this first section you will
use ds9 to make and color an image, and to look at some features.
One of the great things about Chandra is that both of its x-ray
detectors can record really good position information. Because
of this, the first thing we typically want to do when studying
an object using Chandra data is to look at an image of the object.
We call this a "qualitative" look because we are asking
you to notice characteristics of the data that you can see by
eye, without doing any complex numerical (quantitative) analysis.
Don't underestimate the value of taking a qualitative look at
new data: the human eye is a wonderful instrument that can pick
up subtle features of data, providing invaluable insights into
where to look further with more quantitative methods.
Loading the Cas-A image
To load the Chandra image
of the supernova remnant Cas-A, start up the ds9 imaging system.
You will see a window similar
to the one to the left.
Click on Analysis
on the menu bar. You'll notice a dashed line at the top of the
drop down menu. Click on this line to keep the DS9 Analysis window
opened on your desktop.
The DS9 Analysis
window includes several quantitative analysis tools you will
use at various times during the tutorial.
Choose the Virtual Observatory
to access images from various sources.
For this tutorial, you will
need to open the Cas-A supernova remnant image which is located
on the Rutgers X-ray Analysis Server.
Place a checkmark in the
box to the left of the Rutgers server.
Load the Cas-A image from the
list of images shown.
A window indicating that
you have loaded the image of interest will appear.
Minimize this window so
that you can load other images from the list at a later time.
When you have successfully
loaded the image of Cas-A the image will appear as it does here
with the following default settings:
grey color
contrast = 1
bias = 0.5
linear scale
This is the same Cas-A data set that you can load through the
Activities
and Images section. If the image does not load, check to
make sure that you have:
installed ds9
started ds9 and
connected to the Chandra
analysis tools through the virtual observatory on the ds9 pulldown
analysis menu.
If you think you missed
a step, go back to the links on the top
installation page and check to be sure that you have completed
parts a, b and c of Step 1. If you are still having a problem,
contact SAO R&D.
You will want to follow the directions in this section while
working primarily in the ds9 window. We suggest that you print
this section and use the printout as your reference for working
in the ds9 window.
Looking at an X-ray image
More on Contrast &
Bias
Contrast refers to the rate
of change of color with color level. At low contrast, color changes
gradually over many color levels, while at high contrast it can
change rapidly within a few levels. Contrast adjustment works
whether the image is in black and white, or in color.
Bias refers to any offset added to the color levels before the
color map is applied. Changing the bias corresponds to translating
the color map with respect to the color levels without changing
the shape of the map. At low bias, low color levels (i.e., low
pixel values) will have non-zero intensities, while at high bias
only high pixel values will have non-zero intensities.
Contrast and Bias
When the image of Cas-A is first displayed, the image is displayed
in shades of black and white, and its features are a bit hard
to see. But try this:
move the mouse into the
window containing the image
press the right mouse button
and hold it down
move the mouse around in
image with the right mouse button pressed
Notice how the picture changes
so that features of the image come in and out of prominence.
Changing the contrast & bias like this is one way that astronomers
get a better view of their data. You should experiment with this
feature until you like the picture that you see. Note that you
can change contrast and bias whether the image is in gray scale
or in color.
- Changing Contrast: Contrast is adjusted by
dragging the right mouse button vertically in the display window.
- Changing Bias: Bias is adjusted by dragging
the right mouse button horizontally in the display window
- Finessing both Contrast
and Bias: Choosing
Color from the menu bar will allow you to access both
contrast and bias numerically. The default measurement for each
is 1.0 and 0.5 respectively. You can increase these measurements
incrementally and apply the changes to the image until the view
of the data meets your needs.
Cas-A remnant image
in he color with:
Contrast
Bias
1.0
6.7
9.0
0.5
0.06
0.12
More on Color Maps
Colors are specified by the
intensities, i.e. voltages, applied to the red, blue, and green
color guns in the monitor of your computer screen. The assignment
of actual colors to color levels is accomplished through the
use of pseudo-color Color Maps. In such maps, any color can be
assigned to any color level, and all image pixels whose values
are binned into a particular color level will have the color
that is assigned to that level. Color maps are designed to highlight
differences among the pixel values. Depending on the levels which
best distinguish the detail one wishes to study, the shifts from
blue to red and red to yellow can be placed at higher or lower
image pixel values and closer together or farther apart. The
changes in color can be made gradual or sharp.
ds9 implements color maps by specifying colors at a few color
levels, and linearly interpolating to assign colors at intermediate
levels. For example, the basic grey-scale color map specifies
no intensity for any color at the lowest color level (black),
full intensity for all colors at the highest color level (white),
with the red, green and blue intensities varying linearly for
intermediate levels. ds9 offers a number of popular pseudo-color
maps as well as a basic grey-scale map.
Color
There are other ways to adjust the image. Try this:
move the mouse to the top
of the ds9 window, over the word "color"
press the left button to
display the color menu options
while pressing the left
button, move the mouse down until you reach an option that you
want to apply to the image
let go of the left mouse
button to select that color option
Now
once again move your mouse into the image, press the right mouse
button, and move the mouse around. See how the colors change,
once again bringing out different features. You are using the
contrast & bias adjustment with color. Try some other color
menu choices until you find a color scheme that you like.
In ds9, the selected color map is displayed graphically in a
"one-dimensional" image below the main display window.
The x-axis corresponds to color level and the display intensity
corresponds to the color assigned to that level.
grey
inverted grey
red
bb
he
i8
Counting Photons
Recall that an incoming x-ray photon is focused by the x-ray
telescope and then hits the x-ray detector that is currently
in the focal plane of the telescope. This can be the HRC or ACIS
(with some gratings options thrown in for good measure). The
x-ray detector then records information about that x-ray photon
for eventual transmission back to earth. If the detector is the
HRC, an accurate position and arrival time are recorded. If it
is the ACIS, an accurate position and energy are recorded, along
with some timing information. To record an accurate position,
both detectors act like a super-fine mesh or grid, recording
the grid element (or "pixel") that the x-ray strikes.
As more and more x-rays strike the detector grid, each pixel
in the grid can be hit by zero, one, or more x-rays. When we
display this initial image of Cas-A, what we are displaying is
the number of x-rays that were recorded to hit each pixel. Try
this:
In the
ds9 window there is a text table at the upper left. One entry
is "file" and to the right of this is a box with the
file name, in this case, "casa" (Cas-A). Directly below
that is another entry called "value" which has a single
box to its right. Still below are two entries called "physical"
and "image". They each have two boxes to the right,
labelled "x" and "y". Watch those boxes while
you move your mouse around the Cas A image.
You will
see both rows of "x" and "y" values change
as you move your mouse. The differences between the two titles
do not matter for this exercise, and all subsequent x,y values
will refer to the numbers appearing in the "physical"
row. That pair of numbers together are the x,y coordinates that
identify each individual pixel of the detector. As you move the
mouse, the "physical" table is telling you which pixel
of the detector you are located in.
The "value"
shows the number of x-ray photons that were recorded at that
pixel position.
Note that
you can use the arrow keys on your computer to move the mouse
one pixel at a time in any direction, so that you can see the
values change slowly over small regions of the image. There is
a smaller window in the upper right side that shows a magnified
view of a portion of the image around your pointer location.
You can use this window to "zone in" on a specific
area of the image.
Pick a
particular pixel by its x,y coordinates (image value), for instance,
the pixel for which the physical x,y value is 4158,4398. Move
your cursor around until you figure out which way the grid coordinates
are oriented. Hint: This pixel is located in a nice bright spot
in the upper left part of Cas-A. Note that the "value"
at that pixel is 92. Ninety-two is the numbers of x-ray photons
that were recorded to strike that pixel.
More on Scaling
Binning Pixel Values
by Scaling
In order to display a large range of pixel values with a limited
number of color levels (typically 256), image data must be binned
according to some scaling function. A number of different functions
are supported, including:
Linear Scaling: The range of pixel values is
divided by the number of color levels to determine the range
of pixel values for each color level. The fixed range is applied
to mapping all pixel values between the minimum and maximum pixel
value.
Log Scaling: The distribution of pixel values
to color levels is based on the distribution of exp(n) from 0
to X, where n is a parameter (the ds9 default is 10.0) and X
is determined by n and the two ranges (pixel and color level).
Positive values of n favor the lower pixel values, while negative
values of n favor the higher pixel values.
Square Root Scaling: The distribution of pixel values
to color levels is based on the distribution of X^{1/n} from
0 to 1, where n is a parameter (the ds9 default is 2.0) and X
varies from 0 to 1 in steps determined by the number of color
levels. Values of n greater than 1 favor the lower pixel values,
while values of n less than 1 favor the higher pixel values (negative
values and 0 are not allowed).
Image Manipulation & Pixel "Value"
Doesn't changing the colors and/or contrast change the data?
Not at all. Try this:
Change
the color map with the color menu, or change the contrast by
moving over the image with the right mouse button pressed. Go
back to the x,y location of 4158,4398 in the "physical"
line. What "value" is displayed? Again it is 92. Why
is this?
ds9 is
not changing the value of each pixel when you change colors.
Rather, it is simply changing the color assigned to that given
number of photons. When the grey colors are used, then ds9 assigns
grey colors to pixel values ranging from 0 (black) to 255 (white)
When the
contrast is changed, the assignment of colors is changed, not
the data values. You can see the rough assignment of color to
pixel value in the color bar under the image.
Watch what
happens to the color bar while you change the contrast (right
mouse button) or the whole color scheme (color menu).
The color
bar can be roughly divided into 256 pieces, each of which is
assigned a color corresponding to 256 possible pixel values.
What happens if a pixel has more than 256 x-rays and therefore
a value of more than 256? (see More on Scaling in the side bar)
Closing an Image
When you
are finished using the Cas A image, clear the frame by using
the "Clear Frame" command. You will find this in the
main "Frame" pull down menu at the top of the ds9 window.
You can also click on Frame in the lower "short cuts"
menu bar and the Frame options will appear on the bottom line.
First Look, Summary
Astronomers use different colors and contrasts to make the features
of an image easier to recognize by eye. This sort of "first
look" qualitative analysis of data is very important, because
it gives direction to further investigation. ds9 supports a number
of other qualitative techniques that you can learn to further
investigate an image.
Part 2: More Features for Qualitative Analysis
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