Almost any cheap lens can magnify something - but cheap optics
produce fuzzy and/or distorted images. One usually gets what they
pay for in optics, and the extra money spent usually results in
sharper, more accurate images - even with extreme magnification.
What your optical dollars buy:
Resolution is the ability to discern fine details. For image
systems, it is expressed as a dimension - objects separated by more
than a certain dimension will be imaged as separate objects. If
you have a point light source on one side of a lens, the opposite
side will show an image of the light. The produced image will have
the appearance of a larger diameter - because of the diffraction
of light from the edges of the lens. One important factor in the
resolution available from a lens system is it's size. The Abbe
equation for resolution is:
= (Wavelength of Light * 0.61) / (Numerical Aperture)
Numerical Aperture = (index of refraction of the optical medium
between the object of interest and the lens) * Sin (half of
the acceptance angle of the lens)
The Numerical Aperture (NA) is one way to describe the quality of
a lens. The NA is derived from the size of the lens, its working
distance, and it's index of refraction. High-quality objective lenses
indicates their Numerical Aperture on the sides of their barrels.
In general, the useful magnification of an objective is 1000 times
its Numerical Aperture. (A 40x objective with a NA of 0.65 has an
useful magnification of 650 times.) If you magnify beyond 1000 times,
you get fuzzy (useless) magnification. Primarily due to Optical
Aberrations, actual resolution will be less than what the calculations
predict. Aberrations are optical imperfections that impair the resolution
performance of a lens. Of the many different types of aberration,
a few important ones are:
Chromatic aberration is the inability of a lens to focus
different colors of light onto the same spot. The shorter the wavelength
of light is, the more it will be refracted by an optical surface.
As a result blue light has a shorter focal length then red light.
The picture shows a lens focusing a white light point source. At
the point where green light is focused, the red and blue light is
Spherical aberration occurs when the edges of a lens refract
more light than the center. At the area where most of the optical
rays focus together, an image forms a disc - the circle of "minimum
confusion". The effect of spherical aberration is that if you view
an image of a point source, it will have a diffuse halo around it.
While it is possible to add a compensating lens to correct this
effect - it is usually only effective for a particular wavelength
(color) of light. More expensive lens systems compensate for more
Other aberration sources:
Curvature of field occurs when a lens focuses on round (not
flat) objects. Pin Cushion and Barrel distortion occurs
because when an object moves off the optical axis (the center of
the lens system), the focal distance to the lens is farther. This
causes an image magnification error - either a pin cushion or barrel
distortion. Like the other kinds of aberration, this can be minimized
when the design includes compensating lenses.
There is a strong relationship between the amount of aberration
a lens will display, relative to its Numerical Aperture. Typically,
the optical aberration increases relative to the cubed power of
the NA. If you increase the diameter of a lens, the theoretical
resolution increases, while aberrations erode the image quality.
This effect depends on the quality of the lens - a high-quality
lens allows you to use the full Numerical Aperture. Achromat
lenses let you use about 70% of the lens' NA. Apochromats
lets you use 95% to 100% of its NA.
If you can resolve fine details, you can magnify them. Every optical
system has a finite resolution - if you magnify objects beyond the
resolution limits, the results will be useless. Typical resolution
limits of achromat lens objectives:
Another important attribute of any lens system is its Depth of
Focus. Depth of Focus (DOF) is the length of the area (in front
of and behind) the object of interest that stays in acceptable focus.
The single most influential parameter determining the DOF of a lens
system is its Numerical Aperture. The diagram shows a lens at a
full (unrestricted) aperture opening:
On the right side, the focal point is a vertical line - at the
object of interest. As you can see, there is horizontal area showing
the range of acceptable focus. The acceptable Depth Of Focus is
dependent on magnification. generally, the higher you magnify an
object, the smaller the depth of focus.
In the diagram below, the Numerical Aperture of the lens is stopped
down by use of an aperture ring. This decreases the angle of acceptance
- the rays of light enter at a shallower angle, which causes the
Depth Of Focus to increase. (The focal length of a lens is also
a factor affecting DOF - since the angle of acceptance is dependent
on the focal length, which in turn determines the NA.)
A lens with a short focal length will have a small Depth Of Focus.
(A microscope can have a DOF of less than 1 micrometer.)
Another attribute of a lens system is its Contrast. Resolution
is worthless without contrast, the ratio between the dark and the
light - the number of shades. The highest contrast picture will
have only two shades - black and white. The more shades, the less
contrast - but the more information, in the form of an increased
dynamic range. Color is also a form of contrast - the more colors
and shades a computer picture has, the more memory it will take.
In standard (Bright Field) "cheap" optics, contrast and
resolution are usually mutually exclusive. In quality optical systems,
there are several mechanisms that can be used to improve contrast.
Most optical systems are bright field, which makes use of absorption
contrast - the same mechanism as in normal human vision. Light is
absorbed by the object of interest, and that absorption reduces
the light reflected back to the eye/imaging sensor.
Diffraction contrast is when light hitting the edge of the
object of interest bends and is diffracted out of the optical path.
This is the mechanism that enables Dark Field optical systems.
contributor to the performance of a lens system is its Illumination
System. The higher the magnification, the more light required.
The attributes of an optical system (Resolution, Aberrations, Depth
Of Focus, Contrast, and Lighting) trade off against each other.
Resolution and brightness is antagonistic towards contrast and DOF
- you can't have maximum resolution and maximum contrast simultaneously.
If you had an infinite powerful resolving system, there would be
no contrast to allow you to see the image. For an existing optical
system, the iris is usually the most direct adjustment to
make things work best.
The objective lens is the lens closest to the object of
interest. It is the information-gathering lens of an optical system
- the most important lens of a microscope. There are several types
of objective lenses. - the most common and inexpensive is the achromat.
The achromat is corrected for spherical aberration for only the
color green. The achromat is corrected for chromatic aberration
at two different colors.
The apochromat objective
is superior and expensive. Chromatic aberration is corrected for
the three primary colors, and it is spherically corrected for two
colors. Apochromat objectives often require a special compensating
eyepiece. Semiapochromat objectives have correction in between
the apochromat and achromat. Flat field or plano objectives
compensate for curvature of field, and are excellent for applications
where distortion of the image cannot be tolerated. The flat-field
objectives can be constructed to be also an achromat, semiapochromat
or apochromat. This type of combination lenses is always expensive.
Each objective has information about the maximum resolution possible
- written on the side of the barrel. (E.g, on the side of a lens,
is written something like "40X PLAN 0.61 160 / .17".) Generally
the magnification is printed in the largest text, with the manufacturer
type designation. The second value is the numerical aperture. Beneath
that, in a smaller font, the tube length and the cover glass thickness
is given. Other information could be added such as if its an oil
lens, infinity focus, etc.
tube length is usually 160 - the distance between the objective
and the eyepiece, in millimeters. This distance must be maintained
to correct the lens aberrations. On a good microscope, when adjusting
the interpupillary distance (between your eyes) the eyepiece will
extend to maintain the correct tube length distance. The coverglass
thickness (usually around .17 mm) is also important. The more sophisticated
objectives have a coverglass compensation control - so that you
can dial in the thickness of the coverglass.
Objectives for Photomicrography:
When hooking up a camera to a microscope there are many objective
choices. Some objectives are *very* expensive. Do you need to spend
money on a new objective for your application? It depends on how
demanding your application is...
The best quality color photography results are obtained with "Planapo"
planapochromat objectives. Planapos have the highest correction
- corrected for four colors chromatically and spherically. For their
magnification, the Planapos have a higher numerical aperture than
objectives with lesser correction. Planapochromats are the best
objectives for critical resolution and color photomicrography. Other
things being equal, they usually have a shallower depth of focus.
They are very expensive.
Almost as good as the Planapos are plan-semi-apochromats
(also called PlanFl, planfluorite, Fluars, or Neofluars) objectives.
These are also corrected for four wavelengths, but not as completely
as planapochromats are. They provide excellent results, although
they are expensive.
Planachromats are similar to achromats - but have the benefit
of correction for flatness of field, 3 wavelengths chromatically,
and 1 or 2 wavelengths spherically. In white light, these give satisfactory
images for color photomicrography - but not as good as objectives
with better corrections - at a reasonable cost.
Achromats have color correction for two wavelengths of light.
For photomicrography, these inexpensive objectives are best used
in monochrome cameras - they give their best images in green light.
iris diaphragm is the most important single control of any optical
system. This should not be used to regulate the amount of light
- use the light intensity control to adjust the brightness. The
iris diaphragm is the resolution verses contrast control. It does
this by varying the size of the numerical aperture of the objective
lens. It also controls the depth of focus.
Camera lenses have the iris diaphragm built into the objective
lens. In a microscope objective, the iris diaphragm would be so
tiny that it would be hard to manufacture. On a microscope, the
iris diaphragm is placed at the optical "equivalent" of being inside
the objective lens
The eyepiece is basically a projection
lens system. The most common type is the Huygenian. This
eyepiece is used with low to medium magnifications, and is designed
to project the image into a human eye. Some of these eyepiece will
have a long eyepoint (the spot there your eye should be) so you
can focus with your glasses on. Another type of eyepiece is the
compensating eyepiece, and is used with special (apochromat
or flat field) objectives. These provide superior image quality.
Another important type of eyepieces is the photo eyepiece
- designed to project a corrected image onto a camera's film plane.
All eyepieces have a relative magnification - written on the side
of the barrel. They range in magnification from 2.5 X to 15 X -
with the lower magnifications used for the photo eyepiece. Photoeyepieces
(also called projection lenses) have low magnification powers because
the images they project onto film or sensor is usually further enlarged.
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