Diverging, Attenuating Light Rays

This option offers correction for a cominbination of light sheet attenuation and divergence of nonparallel light rays. For good quality images this will generally be the most appropriate choice of correction. If the light rays cross (as they come from a light source which is physically large) then [F Diffusing, diverging, attenuating rays] may provide a more appropriate correction.

We assume the intensity of the sheet P decays in the normal manner, viz:

           dP = -A P ds

where A is the attenuation rate of the dye which will generally be a linear function of the concentration. The observed intensity p is assumed linearly related to the sheet intensity through

           p = F P

where F is the fluorescing efficiency which may be a function of concentration and light intensity.

We ignore any attenuation of the fluoresced light. For weak concentrations we may take

           A(C) = a C
           F(C) = f C

Combining the expresions for dP and p we see

           dP = - (A/F) p ds = - E p ds.

For ideal dyes, both A and F will be linear functions of the concentration C, and so E=A/F will be a constant. Here however we generalise this slightly by allowing E to be a function of the intensity. This function may be obtained from a calibration image containing a uniform dye concentration C0. For the observed intensity field p0 we take a linear approximation such that at each point we estimate E from p0 as

                 1  dq0
           E = - ÄÄ ÄÄÄ
                 q0  ds

where q0 is a smooth function fitted to p0 and averaging in the direction perpendicular to the light rays. The form of the function q0 is

                             2     3
           q0 = a EXP(bs + cs  + ds ),

where the constants a, b, c and d are obtained by a least squares routine. Note that for an ideal dye with no divergence of the light rays we expect

           q0 = a EXP(bs),

with b<0. The additional terms allow for the nonideal nature of the dye and for divergence of the light sheet.

In addition, the nonparallel nature of the light sheet is catered for by integrating in the direction of the light rays rather than simply along pixel rows or columns.

The final step in the correction is to calculate the concentration as

           C = p/P.

NOTE: Before applying this correction, the image intensities should be mapped onto a linear intensity scale passing through zero.

Correct LIF image in which buffer ?

This entry specifies the buffer containing the LIF image to be corrected for attenuation in the light sheet.

Store (first) corrected LIF image in which buffer ?

This entry specifies where the final corrected LIF image is saved. This buffer may be the same as that containing the original image. If more than one buffer was specified in the source list, then the second and subsequent images are stored in sequence starting at this buffer.

Store illuminating intensity in which buffer ?

During the correction process the intensity of the illuminating light sheet is determined. This entry specifies the buffer into which it is written. If more than one buffer was specified in the source list, then this buffer will be reused for each subsequent image.

Constant concentration LIF image (used for calibration) is in which buffer ?

To calibrate the concentrations and determine the diffusion and attenuation of the light sheet it is necessary to capture an image of the set up containing a constant dye concentration. This entry specifies the buffer in which such an image may be found. This image is also used to determine th intensity of the light sheet where it enters the flow. The intensity of this sheet is normally set to P/C0, where P is the intensity of the constant concentration image at the entry point, and C0 the concentration (see next entry). However, if this would result in saturation of the image, then the intensity of the sheet will be rescaled to avoid this (a message to this effect is also produced). Note that this image should have been previously corrected for the camera/VTR intensity transfer function.

Concentration for calibration image ?

This entry specifies the concentration associated with the calibration image stored in the buffer indicated by the previous entry. Concentrations should be in the range 0 (no dye) to 1 (maximum dye concentration).

Correct in Window or whole Screen ?

The image may be corrected in either a window (<W>) or the entire frame buffer (<S>). Note that it is essential that the whole height and width of the window contain a valid LIF image otherwise the fitting of the light sheet will not function correctly.

Window Selection: Region to correct for light sheet attenuation

If the user choses to correct for light sheet attenuation in a window, then the Window Selection submenu is produced to aid the window specification process. Additional information on window specification is available through the [H Help] option within the submenu.

Light rays entering flow at Bottom, Top, Left or Right ?

The direction in which the light rays are travelling must be specified in order to calculate the correction. At present DigImage requires the light rays to be (approximately) parallel with the pixel coordinate system, and the intensity uniform at the boundary of the screen or window through which they enter. Care should be used when applying this algorithm to situations where the light rays are not parallel.

Use which buffer for defining ray directions ?

This entry allows selection of a suitable buffer for defining the orientation of the light rays entering the field of view. Often the ray directions are most easily established by masking of a number of narrow strips in the light sheet such that a grid of lines is projected into the tank containing a uniform fluorescein concentration. An image of these lines will then clearly define the orientation of the light rays. Note that with a good light sheet the rays should not normally be obvious in a uniform dye concentration!

Cursor Positioning: Entry point for ray

    The Cursor submenu is produced to allow each entry point for a diverging
    light ray (such as that marked by the shadow cast by some slide or mask)
    to be specified. The point chosen should be at or near the boundary of the
    image through which the light ray enters. For assistance on the use of the
    cursor, consult [H Help] within the cursor submenu.

Move ray: <left>-, -<right>, change Step size, Manual or Quit ? .52 Move ray: <up>, <down>, change Step size, Manual or Quit ?

    This selection allows the orientation of the light rays to be specified.
    The left and right or up and down arrow keys move the ray in the
    appropriate direction. <S> may be used to toggle between steps of one and
    sixteen pixels at a time. Once the triangle is positioned, <Q> continues
    execution. From a command file it is more convenient to enter the rays
    manually using <M> which prompts for the angle to the nominal ray
    direction.

{If ray direction entered manually}

Angle of rays to nominal direction ?

This prompt is produced only when the ray directions are entered manually rather than interactively. The mean ray angle is specified relative to the nominal ray direction (the nominal ray direction is normal to the side of the image through which the ray enters). The angle should be specified in degrees.

Specify another ray triangle ?

    Between four and ten ray triangles may be specified. They will
    subsequently be used to generate a least squares mapping of the spread of
    the light rays. The first three times this prompt is produced only the
    "yes" answer <Y> will be accepted, thereafter either yes <Y> or no <N> is
    valid.

Message:
Determining light sheet intensity...

Correcting image for light sheet...

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DigImage User Documentation

Stuart Dalziel, last page update: 19 February 1996