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Microscope Fundamentals

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Aberrations - spherical, chromatic Mainly from incorrect geometries and diffraction changes with wavelength. Compensate vs correct
  • correction == positive correction in a downstream optic for upstream optic deficiency.
  • compensation == inverse correction downstream to cancel upstream optic over correction.
Chromatic Aberrations (CA)
  • Correcting optics have blue interior and yellow exterior CA;  reversed in compensating optics.
    Correcting aberrations is typically accomplished by combining different simple lenses.
    Finite compound microscope objective aberrations are typically corrected in eyepieces,
    with mismatches problematic above N.A. >0.6 or so.
    AO, Reichert, Zeiss and Leica infinity objectives expect corrections in tube lens.
    Nikon CF and modern Olympus infinity objectives expect no further corrections;
    telephoto camera lenses can substitute for their tube lenses.

Aperture - effective/working, equivalent, pupil ratio, vs numeric (N.A.)
    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.
    numeric:  N.A. = n * sin(α), where n is (1.0 for air) index of refraction

  • "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

  • Camera + Microscope Combinations - photomacrography.net FAQ
  • Condensers:  achro, aplanatic, Abbe;  finite vs infinity
    Conjugate focal planes - Compound microscope rays Worth watching:  Abbe's experiments and conjugate planes
    8 interleaved focal planes:
    Specimen image at:
    (F1)field diaphragm, (F2)stage, (F3)intermediate image plane, (F4)retina (or camera sensor)
    Illumination source image at:
    (A1)lamp filament, (A2)condenser aperture, (A3)objective back focal plane, (A4)behind pupil
  • Contrast and non-image-forming light:  Köhler
    Correcting eyepieces or tube lenses

    Unlike e.g. Nikon or Olympus, Zeiss and Leica infinity objectives want tube lens corrections.

    The right combination of objective and eyepiece

    Higher objective magnifications are increasingly liable to optical aberrations,
    but greatly reduced in modern larger and more complex infinity objectives,
    while earlier systems applied finite objective corrections in compensating eyepieces.
    Even highly regarded apochromatic finite objectives were undercorrected for lateral color aberrations.
    Perhpas lower power finite objectives have aberrations deliberately introduced for compatibility...?

    cmtalb01 tested correction eyepiece and 40x Zeiss objective combinations:

    Notes:
    • "KPL" and "CPL" are Zeiss;  "CPL" is "clinical plan" = good enough for eveyday routine use
    • "C5" is a Zeiss C5X eyepiece recommended for achromats, not more highly corrected objectives.
    • FK and NFK are Olympus
    • CFW eyepiece is Nikon (no corrections or compensations)
    • "DIC" is a Zeiss Epiplan objective;
      relatively wide compatibility suggests that 0 coverslip objectives provoke fewer aberrations.
    • Hoff M is (probably Nikon CF-based) Hoffman modulation 40X
    • "Neo" is Zeiss Neofluar
    • "HD" is Zeiss Epiplan darkfield
    • "Phase" is probably Zeiss (since compatible only with Zeiss KPL eyepiece)
      With phase contrast optimized for green light, chromatic aberrations are less of an issue.

    As might be expected, a CFW eyepiece (applying no corrections) worked poorly with most Zeiss,
         but OK with a (perhaps Nikon CF-based) Hoffman modulation 40X.

    Coverslip thickness error impact vs N.A.  

    Systematic impact suggests mitigating modest aberrations (e.g. from wrong slide coverslip)
      by deliberately changing tube length...
    This would provoke magnification changes and refocusing inconvenience.

  • Depth-of-Focus scaling:  DoF2 = DoF1 * (f/#2/f/#1) * (m1/m2)**2
  • Diopter vs focal length:  divide 1000mm by focal length, e.g. diopter = 2 for 500mm fl
  • Empty magnification:  Numeric Aperture and Rayleigh's criterion
  • Finite tube length error impact on aberrations
    Floaters
    Note that Lamp Filament conjugate plane (A4) is inside the eye:


    Vitreous Strands are liable to be illuminated.
    Different eyepiece relief can move Lamp Filament conjugate plane, affecting floater visibility.
    Illumination   - internal vs external;  brightfield vs darkfield
      - Köhler illumination
      - diascopic (thru specimens) vs episcopic (above objects):
     
      compound microscope with both episcope and diascopic illumination
    Lens formulae simple
  • 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),
    ...where:
  • 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.

  • Magnification:  Classic compound microscope
  • Nikon's extensive Interactive Tutorials
    Objectives:  Finite vs infinity Bill Otto explains lenses and ray diagrams

    Objective resolving power depends only on N.A., not magnification
    A 20x 0.75 infinity objective at 40x with a 400mm tube lens,
    has no degradation relative to a 40x 0.75 with a 200mm tube lens.
    At specified focal lengths, objectives vary by useful field circle diameters.
    Before 1980, 18mm was typical;  modern Plan objectives can be 22mm or more.

    Finite-conjugate microscope with standardised tube length and infinite-conjugate microscope with standardised tube lens
    Finite-conjugate microscope vs. infinite-conjugate microscope with tube lens.
    from:  Systematic design of microscope objectives
    A finite objective's correction is designed for that tube length,
    with many objectives also depending on both coverslip glass and eyepiece for corrections.

    More explanation

    The upper diagram approximates (RMS == Royal Microscope Society) microscopes;
    with Pupil also called objective's rear conjugate or back focal plane.
    The lower diagram also applies for some modern finite microscopes,
    with Objective + Infinity space + Tube lens combined as a compensated "finite" objective.
    While infinity objectives may be used with a tube lens of any focal length,
    specified magnification depends on that focal length.

    Contrast and non-image-forming light.

     While lenses focus images on your retina or other sensor,
    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.
    Properly (Köhler) aligned conjugate image and illumination planes also improve contrast.
    Some non-image-forming light can be blocked by an iris diaphragm, as in this diagram:
    light field microscope diagram
    Ignore Microlens Array.
    Relay part is afocal photography, where Field Lens is the eyepiece or ocular.

    Objective standards - DIN:  45mm parfocal distance

     Vignetting - infinity microscope Rays from an infinity objective are only parallel when from a single point;
    with increasing distance between objective and field lens,
    a larger field lens is needed to avoid vignetting:

    An objective's back focal plane is where parallel rays entering that objective focus.
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