Estimation of Tube Length
with the
CMOS-Pro Digital Camera

Bausch & Lomb does not mention the tube length of the Research Metallograph [I] in the sales literature.  This is my attempt to figure it out while using the CMOS-Pro digital camera.  The problem is made more complex by the camera adapter, which permits me to adjust the projection distance.  The internal tube length of the metallograph is set by the internal dimensions of the microscope and the eyepiece holder, both of which I have left unchanged.  I have set the projection distance to just barely cover the CMOS sensor of the camera. On my screen, the 480-pixel widths of the stage-micrometer images are each 117mm.  The 0.001 inch line spacings are 10.0mm at left and 11.0mm at right, making the respective overall magnifications 394X and 433X.  The intended tube length for the 40X Balphot I (i.e., Trivert) objective used for the right-hand image is 215mm.  The image width depends on your monitor's pixel size, of course; the ratio between magnification and image width is the constant quantity. Using the nomenclature and formulas given at this link, the focal length of the 3.2X eyepiece is 25/3.2 = 7.81mm, and the focal length of the 40X objective is 215/40 = 5.38mm.  The focal length of the 41X Research I objective is proportionately shorter at 40/41X5.38 = 5.24mm.  I'm not using 215mm yet for calculating the present arrangement, because it's not being used in the Balphot metallograph.  Of course, the focal length of the objective hasn't been altered by plugging it into the Research I metallograph.  I should note now that the 40X objective is mounted on an Olympus Neo10 Nomarski prism mount, which in turn is adapted to a Research I objective holder, which increases the tube length.  The projection distance D for each image here is about 90mm. For  the 41X  Research I objective,  the effective tube length is 394X5.24X7.81/90 = 179mm.  For the Balphot I objective, the effective tube length is 433X5.38X7.81/90 = 202 mm.  I should therefore have raised the Balphot I objective by 13mm in its mount on the adapter between the Nomarski prism and the modified Research I objective mount to obtain the 215mm tube length for which it was designed.  Let that be a project for another day, the work to include a more precise measurement of D. The images below were made with a green interference filter and converted to greyscale before adjusting contrast and brightness.  Right-click on either one to view it actual size in a separate browser window.  Alternatively, left-click to open the original image (compressed according to JPEG - a TIFF image times out my Firefox browser window) in a new browser window. Happily, note that there is hardly any distortion of magnification in these two images (the apparent distortion of the line widths is the result of the large boost in contrast and brightness that was made - see the original images).  From my experience with the use of larger film formats such as the Polaroid Type 55 (4.5 by 3.5 inches) the magnified image at the film plane seemed to be a smaller fraction of the field of view than I have used here.  Therefore, the present approach to image formation achieves a larger image at the nominal 500X magnification for the 41X Research I objective than did the larger Polaroid film format: W = (500/394)X(117/25.4) = 5.85 inch (by 4.55 inch) a 69% greater image area at the same magnification. A similar calculation for the 40X Balphot I objective yields a 500X image size of 5.32 by 4.13 inches.  The smaller  projection-lens magnification made possible by the smaller format of the digital camera is what makes the use of the smaller eyepiece magnification possible.  A standard Bausch & Lomb 10X negative amplifier doesn't work in my setup because its projected image more than covers the CMOS-Pro's CCD sensor at the minimum offset distance - the projection distance would be about 30mm - and its record of severe pincushion distortion is already well known.