Density from Refractive Index Perturbation
Density from Refractive Index Perturbation
The fundamental purpose of this option is to determine perturbations to a
refractive index field. In most cases the refractive index field will be
due to some stratifying agent (e.g. salt or heat) and a knowledge of the
refractive index field can be used to infer the density field.
The perturbations to the refractive index field are determined by
determining the apparent displacement of a regular array of dots. This
displacement is due to gradients in the refractive index field in the
viewing plane. The dots should be aligned carefully with the video camera
and have a spacing of between 8 and 16 pixels in each direction. Ideally
the dots should cover no more than 30% of the area and should be spaced
further apart than the expected apparent displacement. The dots will
normally be positioned some distance behind the tank to be visualised. The
further behind the tank, the larger the apparent displacement will be for
a given refractive index gradient. In this way the sensitivity may be
selected for a given experiment.
Base (unperturbed) image ?
The buffer specified here should contain an image of the dot grid obtained
prior to the initiation of any perturbations to the density field. In
preference, this image should represent a time average (e.g. using [;TA
Time average]) to reduce the noise content.
Process which buffer ?
This entry specifies one of the buffers in which the window centroids are
to be located. Any valid DigImage buffer may be specified. A copy of
this buffer will be displayed while the centroids are being located, and
the displacement vectors will be superimposed upon it.
Determine density perturbation in Window or whole Screen ?
The density perturbation may be determined from the dots in either a
window or the entire buffer. In most cases, a window should be selected.
Window Specification: Region to determine density perturbation in
The windows submenu is produced to allow interactive specification of the
region(s) for which the density perturbation is to be found. This window
should contain the background dots and the boundaries should nominally
fall half way between a column or row of dots. For further details on how
to utilise the window submenu, refer to [H Help] within that menu.
Dot intensity Less than or Greater than background ?
This specifies if the dots are brighter or darker than the background.
Determine dot spacing automatically ?
Selecting Yes will get DigImage to determine the dot spacing automatically
within the specified window. The dot spacing determined is returned in
!!R0 for the vertical and !!R1 for the horizontal. If No, then you will be
prompted for the dot spacing.
{If manual dot spacing}
Spacing of dots in vertical direction ?
Enter the nominal dot spacing for the vertical (i) direction.
{If manual dot spacing}
Spacing of dots in horizontal direction ?
Enter the nominal dot spacing for the horizontal (j) direction.
Allow automatic adjustment of dot spacing in Both directions, Horizontal or
Vertical directions, or No adjustment ?
Often the dots detected will not follow exactly the nominal spacing
determined either automatically or specified by the user. This option
determines whether DigImage may automatically adjust the nominal spacing
between neighbouring pairs of dots to correspond to that actually
detected. In most cases full automatic adjustment (<B>) is desirable. If,
however, the "dots" are in fact lines (such as those used for the
real time synthetic Schlieren method), then the automatic adjustment in
the direction parallel to the lines should normally be suppressed.
Allow displacements in Both directions, Horizontal direction or Vertical
direction?
This option allows either the horizontal or vertical component of the
dot displacement to be turned off and ignored during the calculation of
the density perturbation. In some situations (e.g. small amplitude
horizontal perturbations captured from video tape where electronic and
mechanical jitter lead to less accurate horizontal positioning)
suppression of the horizontal component of the displacement will lead to
an improved signal to noise ratio.
Use Blob or Window centroid ?
The location of the dots may be determined either using the centroid of
the window surrounding the dot, or from the centroid of the "blob"
contained within the window. If the window contains only one connected
region satisfying the threshold, then these two measures will give the
same location for the centroid. However, if more than one region is
detectable within the window, then the Blob centroid is to be preferred.
Note that for the blob centroid to function, it is necessary for the
window centroid to be contained within the blob region.
Mean displacment vectors: Force Both to be zero, X only zero, Y only zero or
both Free ?
This option controls the mean of the apparent displacment vectors. By
selecting <F>, the mean calculated from the images will be used. However,
in many situations we would expect the mean to be zero and any deviations
from this to represent either pixel jitter (especially in the horizontal)
or thermal noise in the laboratory environment. Selection of <B> or <X>
may remove most of the horizontal pixel jitter and improve the quality of
the results.
Reference points: None, use Current mapping or Find in images ?
The accuracy of the displacement field can be improved by making use of
the DigImage permanent reference point facility [;PR: Reference points] to
correct for image jitter. If you wish to use the reference points, then
this option may either use the current mapping function or determine the
mapping functions for the two images automatically (once the reference
points have been set up). If you use the current mapping functions (<C>),
then DigImage assumes these are referenced to the base image (e.g. through
the [;PRT Transfer current locations to reference] mechanism) and you (or
your command file) have used [;PRF Find current reference mapping] to
determine the mapping functions for the image to be processed. If you get
this option to find the reference points, then it will locate them in BOTH
the base and sample images and apply the difference between these as a
correction.
Note that if you are apply a mask to your images prior to analysis, and
you select <F>, then you must ensure your reference points remain visible
after the mask has been applied.
Display density field in which buffer ?
This entry determines the buffer in which the density field (and
optionally displacement vectors - see below) are rendered.
Scale factor ?
This scale factor affects the greyscale rendering of the density field. A
value of zero will force automatic evaluation of the scale factor to
utilise the entire intensity range from 1 to 254 (0 is reserved for the
background and 255 for the displacement vectors, if enabled). In this
case, the scale factor used is subsequently available in !!R2 once
DigImage returns to the menu.
Superimpose displacement vectors ?
This option allows the displacement vectors calculated from the centroids
to be superimposed on the false colour field representing the density.
These displacement vectors are simply the gradient of the density field.
Their presence can aid the interpretation of the density field, especially
if the signal is somewhat noisey.
{If displacement vectors superimposed}
Scale for displacement vectors ?
If the displacement vectors are superimposed on the density field, then
this entry controls how their length is scaled. A unity value will give
the actual displacement of the centroid but, as this is often very small,
may be rendered as a single point.
Display error in density field in which buffer (-1 to suppress) ?
One of the underlying assumptions in this calculation is that the
displacement vectors represent the gradient of the underlying density
field. As such their curl should vanish (since curl(grad ()) is
identically zero). Due to a combination of noise, imprefections in the
experiments and images, three-dimensional effects and the non-parallel
light rays passing through the viewed region all conspire to produce a
displacement field with nonzero curl.
This entry specifies whether DigImage should display the curl of the
displacement field in order to visualise the errors associated with the
calculation of the density field. Note that the manner in which the
density field is extracted from the displacement field is designed to
minimise the errors produced by nonzero curl. The scaling of this image is
chosen to indicate the severity of the error: ????.
Name of output file (.GRD default extension, blank to suppress) ?
The displacement data is written out to the specified file for subsequent
processing by Trk2DVel.
Write displacement vector file (blank to suppress) ?
If specified, the apparent displacement vectors will be written to the
specified file in an ASCII format.
Errors, Warnings and Messages
Using scale factor !!R2=!!GR2...
Deterine optimal window spacing...
Nominal dot spacing !!R0=!!R0 (vertical), !!R1=!!R1 (horizontal)...
Find dots in base image with window spacing !!R0 !!R1...
Reference points found in base image with error !!R4=!!GR4
Compare with new positions...
Reference points found in sample image with error !!R5=!!GR5
Check displacement vectors...
Mean displacements: dx=!!R6=!!GR6, dy=!!R7=!!GR7
Setting specified mean displacments to zero...
Integrate to get density field...
Render density field...
Create .GRD output file...
Create displacement vector .DAT output file...
Evaluate error in density field...
Render vector potential...
Error Message:
Unable to open output file
Parent menu
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DigImage User Documentation
Stuart Dalziel,
last page update: 19 February 1996