Re: 3d reconstruction from stack [SEC=UNCLASSIFIED]

[Goldsmith, Noel]

Andrew Meyer asks about

Subject: 3d Reconstruction from Stack

We have an application where we are taking a stack of pictures of a fuel
injector seat and spray orifices, and trying to reconstruct a 3-Dimensional
image for use in verifying that  the hardware was made to spec.  We are
using a microscope with a short focal length, so that the features in the
stack appear to grow in size as we get closer to the object.  (think of a
star field animation, where the nearer stars go racing to the edge of the
picture as the spaceship goes through the star field).

Noel replies.
Andrew,
It sounds like the images are like those produced with a short focus wide
angle lens. Even a bit like a fish eye.
To successfully use such image series in a Deep field or focus manner, the
images need to be rectified. Which means that distortion needs to be
corrected. Distortion comes from two sources at least. Firstly the variation
in magnification across the field of the image. Secondly I think you are
getting some perspective distortion as well.
There is a distortion corrector/creator for image J, called cubic spline
deformation generator. And there are some others which do other things.
There is also an application or code called Hugin (I think). There are a few
Apps around for producing panoramas from cameras which cope with all of
these things, you either need to know the parameters or  pick up the
camera/lens from the lists.
And further, it seems that the depth of field in your images is large, as
you can see the object getting larger as it approaches the camera.
This is not a good thing if you wish to use a focus criterion to determine
when your image is in focus.
A microscope lens with a numerical aperture of 0.5 will have a depth of
field of around 2-5 microns depending upon how critical you are. But the
working distance might be only 10 mm or so for a Long Working Distance lens.
If you want a precision of around 1 µm then you will need a Numerical
aperture of around 0.8 or better. And getting a working distance of greater
than 1mm or so may be difficult.

A rough guide which converts NA to F number is F = 1/(2*NA). This can help
to work out if the macro or telecentric lens you want to use has any shot at
doing what you need. This also is assuming that the microscope lenses are
good and the macro / telecentric lenses are superb.

For precise work the use of a telecentric lens is recommended. Such a lens
maintains the image size, over a specified range, whether in focus or not.
In addition the image of an object such as a field of vertical pins at right
angles to a plane which is a right angles to the lens axis will show the
tops of the pins, and none of their sides even at the edge of the field.
This means there is no perspective in the image. And also minimal
distortion. Telecentric lenses have large front elements which have a
greater diameter than the field of view.

If you image a graph paper or a rectilinear grid, look at the lines on the
edge. They should be straight. If you the tilt the grid (a known amount) and
repeat the imaging, you can measure the depth of field.

Hope this is useful
Noel

Noel Goldsmith
Air Vehicles Division
DSTO
506 Lorimer Street
Port Melbourne
3207 Victoria
AUSTRALIA
613 96267527
0428364003
[hidden email]
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