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Imaging (Finite/Finite) Image Reduction or Beam Expansion (Infinite/Infinite) Focusing and Collimation (Infinite/Finite)
Description Of Variables
Most application solutions can be divided into three types: Finite/Finite
Conjugate, Infinite/Infinite Conjugate, or Infinite/Finite Conjugate.
A finite/finite conjugate design focuses light from a source (not at infinity)
down to a spot. Most imaging lenses, which take the image of an object at a
finite distance and focus it onto a sensor, work this way. An infinite/infinite
conjugate application takes incoming collimated (parallel) light, changes
the beam diameter according to the magnification, and emits the collimated
light. An infinite/finite conjugate design combines these two processes
by focusing a source placed at infinity down to a small spot.
It is best to begin a design with the “paraxial solution” for which a designer
approximates first order properties such as conjugate distance, image and
object heights, magnification, etc. Paraxial calculations utilize paraxial elements
– theoretically perfect lenses that do not introduce system aberrations
through lens thickness, radius of curvature, glass type and dispersion
effects. Note: the only specifications for a paraxial lens are its position relative
to the image and object plane, lens diameter, and focal length. After finding
the paraxial solution you can begin the best real lens solution which
makes allowances for lens thickness, dispersion effects, etc.
Hi , Ho Image and object height, respectively. This represents HALF of
the actual full image and object size.
I , O Image and object distance measured from the lens closest to the
image and object respectively.
Fi , Fo Focal length of the lens closest to the image and object, respectively.
F Effective focal length of the entire lens system.
d Distance between two elements.
q FULL angle of the cone of light accepted or emitted by a lens system.
ai , ao Angular HALF field of view in infinite conjugate systems.
TP Throughput is the system’s ability to transfer light.
f/# f/# is the lens’ ability to focus/collect light.
D Diameter of lens
Positive Values: The following quantities are expressed as positive values: heights above the optical axis, distances measured to the right of a reference
point, focal length of focusing lenses, and angles that are measured counter clockwise from the optical axis.
Negative Values: The opposites of the above quantities are expressed as negative values (i.e., while height measured above the optical axis is expressed
as a positive quantity, height measured below the optical axis is expressed as a negative quantity).
Reference Point for Equations Given: Lens Position.