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Microscope Basics

  • Another ( attempt at basics
  • Aberrations - spherical, chromatic
  • Aperture - effective/working, equivalent, pupil ratio, vs numerical (N.A.)
  • Camera + Microscope Combinations
  • Canon EF DSLR sensor-to-flange depth
  • Condensers
  • Contrast and non-image-forming light:  Kohler
  • Depth-of-Focus scaling
  • Diopter vs focal length
  • Kohler illumination
  • Lens formulae
  • Magnification:  Classic compound microscope
  • Nikon's extensive Interactive Tutorials
  • Objectives:  finite vs infinity-corrected
  • Zerene focus stacking
  • 1:4 to 8:1 magnification FAQ

    Finite vs infinity-corrected objectives

    To prime your thinking about lenses and ray diagrams, review this explanation by Bill Otto.

    Finite-conjugate microscope system with standardised tube length and infinite-conjugate microscope system with standardised tube lens
    Finite-conjugate microscope system vs. infinite-conjugate microscope system with tube lens.
    from:  Systematic design of microscope objectives
    The vertical dotted line where rays cross at right end of tube length is called the objective's rear conjugate.
    To the extent that it is, a finite objective's correction is designed for that tube length,
    keeping in mind than many objectives also depend on both slide cover glass and eyepiece for correction.

    More explanation

    The upper diagram is supposed to represent a traditional (RMS == Royal Microscope Society) microscope.
    "tube length" is approximately the objective's focal length for its specified magnification,
    if that objective was a simple convex lens.
    The lower diagram, which is nominally about more modern microscopes,
    is arguably also more accurate for some "finite" microscopes,
    if Objective + Infinity space + Tube lens are considered together as a compensated "finite" objective.
    While infinity objectives can be used with a tube lens of any focal length,
    specified magnification depends on that focal length.

    Abramowitz & Davidson "Optical Microscopy"


    Yang & Gross "Systematic design of microscope objectives"

    Contrast and non-image-forming light.

    While lenses can and do allow images to be focused on your retina,
    they do not prevent other photons from also stimulating sensors.
    When viewing a three-dimensional scene, perhaps focusing on a near object,
    photons scattered from more distant objects may also land on the same photosensors.
    Some non-image-forming light can be blocked by an iris diaphragm, as in this diagram:
    light field microscope diagram
    Ignore that Microlens Array. Relay part is afocal photography, where Field Lens is the eyepiece or ocular.

    Kohler illumination:  lamp, field diaphragm and condenser alignment

    Any number of websites will waste space pointing out how important it is,
    then provide miserable, incomplete and wrong instructions.
    Fortunately, Wikipedia does all right;   here are my Kohler experiences.

    Lens formulae

  • 1/f = 1/do + 1/di           {1} di becomes f for infinite do
  • m = di/do                         {2} zero magnification for lens focused @ infinity
    magnification change by focus distance
  • f = (d2 - d1)/(m2 - m1); {3} alternatively:
  • d2 = d1 + f*(m2 - m1)
  • m2 = m1 + (d2 - d1)/f
    magnification for classic (RMS) compound microscope
  • m = (L/fo)*(D/fe),
  • m = magnification
  • L = tube length (160mm)
  • D = normal vision relaxed distance (250mm)
  • f = focal length
  • fo = objective focal length
  • fe = eyepiece focal length
  • di = lens to image distance
  • do = lens to object distance
    For 160mm tube length, a 10x objective has 16mm focal length
    and a 10x eyepiece has 25mm focal length.
    For infinity scopes, substitute "tube lens focal length" for "tube length".
    Olympus infinity objectives expect 180mm tube lens focal length;
    Nikon finite CF BD and M Plan objectives expect 210mm tube length.


  • Spherical lens surfaces are relatively easy to produce, but not ideal.
  • Combining different dispersions and refractive indices can reduce lens aberrations.
    Compensate vs correct
  • correction == positive correction in a downstream optic for upstream optic deficiency.
  • compensation == inverse correction in a downstream optic to cancel upstream optic over correction.
    Chromatic Aberrations (CA)
  • Correcting optics display blue interior CA and yellow exterior CA;  reversed in compensating optics.


    effective (working aperture)
  • Coupled lenses, stopped in the front, with the rear lens focused at infinity:  m * lens aperture
  • Single lens, focused by extension:  (m+1) * lens aperture
  • Teleconverter factor x inserted between camera and all other optics:  x * lens aperture
  • Microscope objectives used as designed:  m / (2 * N.A.)
    equivalent e.g. "How does a 4X N.A. 0.1 objective compare to an f/whatever macro lens?"
  • f=1/(2*N.A.)  is not a bad approximation.
  • A better approximation would be f=1/(2*N.A.) * M/(M+1), where M is rated magnification.

    "pupil ratio" compensates effective aperture for adding extension

    aperture vs N.A. :  N.A. = 1/(2 * f/#)

    f/# 1.2 1.4 1.8 2 2.8 4 5.6 8 11 16
    N.A. .4167 .357 .417 .25 .1786 .125 .0893 .0625 .045 .03125

    Canon EF sensor-to-flange depth:  44mm

    Add to extension tubes when testing lens focal lengths

    Condensers:  achro, aplanatic, Abbe;  finite vs infinity

    Tweaking Abbe condensers
    Abbe flaws begin to bother above N.A. 0.6-7; elevate an Abbe to optimize filling the objective's back lens.

    Depth-of-Focus scaling

    DoF2 = DoF1 * (f/#2/f/#1) * (m1/m2)**2

    Diopter vs focal length:  divide into 1000mm, e.g. diopter = 2 for 500mm fl

    Zerene macro step size tables:  magnification vs frame width, magnification vs aperture

  • magnification m = sensor width / frame width
  • DoF (mm) = 0.0022*(((m+1)*f/#)/m)**2
  • DoF (mm) = 0.00055/(N.A.**2)

    Zerene landscape focus tables

    1:4 to 8:1 magnification FAQ