Optical Design Data
Lens Terminology
The lens is the most basic optical
component. It collects light from a source
and refracts that light form a usable image
of the source. The source may be an
illuminated object or produce the light
itself.
When designing experiments or assembling
systems with simple lenses or lens
combinations, there are a few formula that
are very useful. The following definitions
refer to the singlet lens diagram above. In
the paraxial limits, however, any optical
system can be reduced to the specification
of the position of the principal and focal
point. Shown on this diagram is the
effective focal length (EFL or f), the back
focal length (BFL), the front focal length
(FFL), the center thickness(Tc), and the
locations of the element's principle points
(H1 and H2). The radii of curvature R1
and R2 refer to the
left and right surfaces respectively. R1
or R2 is
positive(negative) if the center of
curvature is to the right(left) side of the
lens. The EFL is positive(negative) if the
focal point is to the right(left).
Focal Length Formulas for Singlet Lenses
& Mirrors
|
Type
|
Orientation
|
Effective Focal Length (f)
|
|
|
|
Lens
|
Mirror
|
|
General |
 |
R1 = R1
R2 = R2 |
|
|
|
Plano-Convex |
 |
R1 = R1
R2 =
 |
R
----
n-1
|
R
- ----
2
|
|
Plano-Concave |
 |
R1 = -R
R2 =
|
- R
----
n-1
|
R
----
2
|
|
Bi-Convex |
 |
R1 = R
R2 = -R |
 |
|
|
Bi-Concave |
 |
R1 = -R
R2 = R |
 |
|
where, n is index of refraction of lens
material
Effective Focal Length of Two Thin Lenses
The following formulas show how to calculate
the effective focal length and principal
point locations for a combination of any two
thin lenses. Calculate the values for the
first two elements, then perform the same
calculation for this combination with next
lenses. The expression for the combination
focal length is the same whether lens
separation distances are large or small and
whether f1 and f2 are positive or negative.
|
f1
f2
f =
-----------------
or
f1
+ f2 - d
1
1 1 d
--- = ---- + ---- -
-------
f f1 f2 f1 f2
|
|
F-Number (F/#)
The f-number (also known as speed) of a lens
system is defined to be the effective focal
length divided by system clear
aperture(effective diameter D). The f-number
defines the angle of the cone of light
leaving the lens which ultimately forms the
image. This is important concept when the
throughput or light-gathering power of an
optical system is critical, such as when
focusing light into a monochromator or
projecting a high power image.
Numerical Aperture (NA)
The numerical aperture of a lens system is
defined to be the sine of cone angle, ,
that the marginal ray makes with the optical
axis multiplied by the index of
refraction(n) of the medium. The numerical
aperture can be defined for any ray as the
sine of the angle made by that ray with the
optical axis multiplied by the index of
refraction :
1
NA = n sin
=
-----------------------
2
• (F / #)
|
Sagitta
The Sagitta (or Sag) of a spherical or
cylindrical surface is an essential value to
calculate when determining the edge and
center thickness of a lens. The Sagitta is
the thickness of
material required to accommodate a surface
of given radius of curvature with a given
aperture. The Sag of surface may be
calculated from :
Using Wedged Window
A problem with parallel substrate is that
the second surface reflection can overlap
the first surface reflection and lead
unwanted spectral channeling through
interference. The higher the parallelism,
the worse the problem. Wedged windows are
laser quality windows manufactured with
wedges of 0.5° ~ 3°. For small angles of
incidence, the deviation of ray incident on
a wedged window with wedge angle
 is
d
= (n-1)
 |
 |
|
Deviation and reflection of a beam
by a wedged window of wedge
. |
A beamsteering wedge formed from two
wedged prisms. |
The first reflected ray is misaligned from
the initial axis by an angle defined by
r
= 2n
To created an adjustable beamsteering
device, use a pair of identically wedged
windows. Any deflection angle from 0 to 2,
can be obtained by suitable rotation of the
individual wedges. The direction of
deflection in along a plane midway between
the rotation angles of the two individual
prisms. The magnitude of deflection varies
smoothly from the maximum value, 2
where the thinnest points of the two wedges
coincide to zero, when the two wedges are
oriented antiparallel, thereby canceling
each other.
Selecting a Prism
Prisms are blocks of optical material having
flat polished sides arranged at precisely
controlled angles to each other. Prisms may
be used in an optical system to deflect or
deviate a beam of light. They can invert or
rotate an image, disperse light into its
components wavelength, and be used to
separate states of polarization. Prisms will
introduce aberrations when used with
convergent or divergent beam of light. Using
prisms with collimated or nearly collimated
light will help minimize aberrations.
|
|
Type
|
Orientation
|
Usage
|
Applications
|
|
|
Inversion
|
 |
The image in an incident beam
emerges upside down, i.e. rotated
180° about a horizontal center line. |
- Image rotation
- Microfilm viewer
- Optical profiler |
|
|
Reversion
|
 |
The image in an incident beam emerge
left to right and right to left i.e.
rotated 180° about vertical center
line. |
- Image reversal
without deviation |
|
|
Deviation
|
 |
The incident beam emerges in a
different direction of propagation.
|
- Range-finding,
surveying, alingment
- Cine photography |
|
|
Displacement
|
 |
The incident beam emerges in the
same direction of propagation but
along a different axis. |
- Periscope systems
- Beam folding
- Stereoscopic
systems |
|
|
Dispersion
|
 |
The incident beam emerges split up
into its constituent spectral
components. |
- Prism spectrometers
- Pre-dispersers in
high power systems |
|
Waveplates
Waveplates operate by imparting unequal
phase shifts to orthogonally polarized field
components of an incident wave. This causes
the conversion of one polarization state
into another. These are two cases.
With linear birefringence, the index of
refraction and hence phase shift differs for
two orthogonally polarized linear
polarization sates. This is the operation
mode of standard waveplates.
With circular birefringence, the index of
refraction and hence phase shift differs for
left and right circularly polarized
components. This is the operation mode of
polarization rotator.
Quarter and Half Waveplates
A quarter waveplate transforms
polarized light between linear and
circular polarization. Input
linearly polarized light must be
incident at 45° to the crystalline
axis.
A half waveplate rotates the
orientation of input polarized
light. The ratation angle is twice
the angle between the incident
polarized light and the crystalline
axis. |
|
|
|
Quarter Waveplate
|
Half Waveplate
|
|
Dual Wavelength & Harmonic
Waveplates
These are multiple order waveplates
which provide specific retardance at
two different wavelengths (ex.
quarter wave at 1064nm and half wave
at 532nm). Dual wavelength
waveplates are offered at a variety
of popular laser wavelengths and
harmonic waveplates are used ar
1064nm and various harmonics.
Dual Wavelength waveplates provide
separation of different wavelengths
with a polarization beamsplitters by
rotating the polarization of one
wavelength by 90°.
These components are particularly
useful when used in conjunction with
other polarization sensitive
components to separate coaxial laser
beams of different wavelength. |
|
|
Polarization Rotators
The optical axis in a polarization
rotator is perpendicular to the
polished face of the optic. The
result is that the orientation of
input linearly polarized light is
rotated as it propagates through the
device. Standard devices offer 45°
and 90° rotation at a number of
common laser wavelengths. Unlike a
half waveplate, the rotation is
invariant to the polarization of the
incident light.
The polarization rotators is highly
dependent(nearly inverse square
ratio) upon wavelength. |
|
|
|