Choosing a lens - What Focal Length is required?

If you want to produce an image of a certain size to fill a CCD (or other image sensor types), this page determines the approximate focal length of the lens required. (There is plenty of tutorial below the calculator section.) CCD sizing issues:

CCDs (and other image sensors) are usually rectangular - not square. Lenses are usually circular - when you put a circle over a rectangle - you must "waste" either part of the rectangle or the lens. Usually you waste part of the lens - making a circle of light larger than, and concentric to, the CCD.

CCDs are measured in "sizes", such as 1/3, 1/2, 2/3, and 1 inch. These sizes are not the diagonal length of the CCD - they are sizing standards based on the old video tube sensors that CCDs replaced. The Horizontal and Vertical (or XY, or WH) are different sizes -the Horizontal could be 768 pixels, and the Vertical could be 493 pixels.

At first glance, optics formulas to determine Focal Length seem to be missing part - the distance (from the lens to the CCD). This "missing" distance is not required because of the standard of "C-mount" camera lenses.

When finding the Focal Length of a lens to use, the optimum Focal Length to completely fill the CCD is different for the H and V. Which do you optimize for? Whatever is important to you. If you have to measure something 2 feet wide, you optimize FL for the H. If your object to measure is 1 meter tall, you optimize the Focal Length for Vertical.

Here are the "fudge" factors to plug in for different CCD sizes (pick either H or V):

1/3-inch CCDs: H = 4.8 mm, V = 3.6 mm
1/2-inch CCDs: H = 6.4 mm, V = 4.8 mm
2/3-inch CCDs: H = 8.8 mm, V = 6.6 mm
1-inch CCDs: H = 12.7 mm, V = 9.5 mm

All entries must be in millimeters - without commas. (If the calculated FL is"NaN," that means it is "not a number" in JavaScript - and the answer is too small for a typical single lens - 3 mm or less.)


(handy) MM/Inch conversions - from: Millimeters Inches (to) Millimeters Inches

Type the number you wish converted here (decimals):




Enter the distance to the thing you wish to photograph, in mm
Enter the size (largest of either width or height) of the thing you wish to photograph, in mm
Enter the size of the CCD area the image should fill, in mm (see below)
Your lens should have a focal length of approximately (in mm):
Java coding courtesy of Philip Stripling, his web site is at www.PhilipStripling.com.


Microscope (and lens) Basics

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:

Resolution = (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 blurred.

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 colors.

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:

Magnification
NA
Theoretical Resolution
(micrometers)
Practical Resolution
(micrometers)
4X
0.10
3.05
3.40
10X
0.25
1.22
1.30
40X
0.65
0.47
0.52
100X
1.30
0.24
0.26

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.

Another 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.



Microscope-Specific Components

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.

The 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

The 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


Eyepieces

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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