How to Select a Multielement Lens
Multielement lenses are used in imaging and focusing
applications requiring a higher degree of aberration
correction than can be achieved using a single lens.
While bestform lenses do an excellent job of minimizing
aberrations in a singlet format, a multielement lens
can provide additional performance benefits, such as
correction over larger apertures, several wavelengths, or a
wider field of view.
Multielement lenses typically consist of two or three
elements, referred to as doublets and triplets, respectively.
These lens elements may be of differing shape, curvature,
and/or material, and may be mated with cement or
mounted with air gaps. Together, they act to minimize
the many sources of wavefront distortion that can result in
blurred or irregularly shaped focal spots, or non-uniform
illumination fields. If a singlet lens is unable to meet
your performance requirements, an achromat, aplanat, or
objective lens may be required.
Fig 1: Spherical aberration and Coma
In order to select a multielement lens, it is first necessary
to understand the types of aberrations that can occur
when a lens focuses light. When these aberrations are
sufficiently reduced for an optic, that optic is said to be
diffraction limited, i.e., its performance is limited more by
the diffraction of the light waves and by the laws of physics
more than by the optic’s design. For example, aberrations
resulting in wavefront errors substantially less than λ/4
won’t significantly affect a telescope’s resolution.
Do I really need a multielement lens?
Types of aberrations
Spherical aberration occurs when rays passing through
the outer zone of the lens focus at a different distance
from the lens than rays passing through the central zone.
It is axially symmetric. Uncorrected spherical aberration
leads to blurry focal spots. Coma is an off-axis wavefront
distortion which increases linearly with field angle. It is
non-symmetric. Uncorrected coma leads to irregularly
shaped focus spots or a change in magnification with field
angle. Chromatic aberration is produced by dispersion,
or the variation of refractive index with wavelength, and
causes different wavelengths to have different focal points.
Astigmatism results in the tangential and sagittal image
planes being separated axially. This is characterized by
a saddle wavefront, and will appear as two distinct focal
points. It is not typically an issue for on-axis applications;
good quality lenses correct for astigmatism.
To determine whether a singlet or multielement lens
is needed to achieve the required spot size, dspot, first
calculate the required focal length (f) from the divergence
properties of the beam.
For a TEM00 Gaussian beam, use:
Eqn. 1
where w0 and wspot (i.e., dspot/2) are the initial and desired
beam waists. This formula is an excellent approximation
when the distance from the initial waist w0 to the front
focal plane is much smaller than the initial confocal
parameter z0 = πw02/λ.
For a non-diffraction-limited laser beam, use:
Eqn. 9
Eqn. 2
Using f/# = f/d0, we obtain the condition:
where Δθfull is the measured or manufacturer-specified full
angle divergence.
For a uniform incident collimated beam truncated by an
aperture d0, where diffraction limited focusing is required, use:
,
Eqn. 3
Eqn. 10
To achieve diffraction-limited focusing, the f/# has to be
greater, or the speed of the single element lens “slower”
than this expression containing the focal length. As an
example, see the figure below. It shows the limiting f/# for
diffraction-limited focusing for a plano-convex fused silica
lens at λ = 514.5 nm.
where the diffraction limit is estimated by the first
minimum of the Airy diffraction pattern in the focal plane.
Next, calculate the blurred focal spot for a singlet lens due
to the spherical aberration (Third Order aberration theory),
using the shape factor (K), index of refraction (n), and
incident beam diameter (d0):
Eqn. 4
,
Eqn. 5
Eqn. 6
For a properly oriented plano-convex lens of index n = 1.5,
the bracketed factor is 0.073.
If the blurred focal spot size is greater than or equal to
the desired spot size, a multielement lens is required to
achieve the desired spot size. The next lens selection
rule is based on blur as a result of spherical aberration
compared with blur due to diffraction. It can also be
formulated as a limiting f/#.
Eqn. 7
Eqn. 8
Fig 2: Limiting f/# for diffraction limited focusing for a planoconvex fused silica lens at λ=514.5 nm
Aplanats
Aplanatic lenses are designed to be free of the two largest
sources of aberration for monochromatic light: spherical
aberration and coma. Together, these two aberrations
distort the transmitted wavefront through the lens and
cause the focal spot to become irregularly shaped and/
or blurred. By correcting spherical aberration and coma,
aplanats exhibit essentially diffraction-limited performance
over their full aperture, and minimize focal spot size.
Aplanats are essential when tight control of the image
and/or focal spot size at a single wavelength is critical
to overall system performance and functionality.
Applications include nonlinear optics experiments, laser
beam expanders and collimators, interferometers, beam
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handling systems, material ablation and cutting systems,
fiber optic interfacing. They can maintain image quality
throughout the beam path, critical in imaging of optical
traps. They are used widely with fiber lasers in material
processing and research due to their ability to generate
more tightly focused beams, higher energy at the work
surface, sharper images for marking, and finer cuts for
micro-machining.
Depending on the overall performance criteria, aplanats
can be designed using 2-3 lenses of the same or different
materials, and can be air-spaced to increase damage
threshold and minimize additional wavefront distortion
induced by the cement between the glass surfaces. Use of
high-energy antireflection coatings can allow an air-spaced
fused silica lens to transmit greater than 98 – 99 % of the
incoming light while still withstanding more than 30 J/
cm2 of pulsed light at 1064 nm. Air spacing also allows for
more flexibility in design, as adjacent surfaces do not need
to have matching curvatures. Instead, each of the four to
six surfaces can be optimized independently, and the air
gap can be treated as an additional lens element in order
to better reduce coma and spherical aberrations through
the complete lens assembly. Bonded lens assemblies
carry their own benefits, including increased mechanical
strength, greater durability, and increased overall
transmission as a result of fewer surface reflections which
are produced by external surfaces.
Aplanat Lens Type/
Product Code
Construction
Elements &
Materials
Our LAP and LAPQ series laser aplanats are air-spaced
doublets designed to produce minimum focal spot size
when used to focus collimated monochromatic laser
beams. They exhibit near diffraction limited performance
over their full f/5 aperture. CVI Laser Optics guarantees
less than λ/4 peak-to-valley wavefront distortion for all
aplanats in the LAP and LAPQ series. This means that the
energy falling within a theoretical circle co-incident with
the minimum of the first dark ring of the Airy diffraction
pattern will contain at least 80% of the energy contained in
the corresponding region of an ideal diffraction pattern.
Fig 3: The graph depicts high quality (10-5, λ/10 TWD) planoconvex (PLCX) and Bestform (BFPL) singlets plotted against an
equally high quality aplanat (LAP) at 1090 nm.
ƒ/#
Wavelength
Range
Surface
Quality
Transmitted Wavefront
Distortion
LDT
Visible Laser Aplanat/
LAP
air-spaced
2 elements:
N-SF11
5
420 - 2000 nm
40 -20
< λ/4 @ 633 nm
over 95% of CA
4 J/cm2, 20 ns, 20
Hz @ 1064 nm
High Energy/UV Laser
Aplanat/
LAPQ
air-spaced
2 elements:
UV-grade fused
silica
5
180 - 2200 nm
10 - 5
< λ/4 @ 248 nm
over 95% of CA
15 J/cm2, 20 ns, 20
Hz @ 1064 nm
Aplanatic Meniscus
Lens for use with
companion LAP/ APM
air-spaced
1 element:
N-BK7
3.3
420 - 2000 nm
(LAP + APM)
40 - 20
< λ/2 @ 633 nm
over 95% of CA
4 J/cm2, 20 ns, 20
Hz @ 1064 nm
UV Aplanatic Meniscus
Lens for use with
companion LAPQ/
APMQ
air-spaced
1 element:
UV-grade fused
silica
3.3
(LAPQ +
APMQ)
180 - 2200 nm
10 - 5
< λ/2 @ 248 nm
over 95% of CA
15 J/cm2, 20 ns, 20
Hz @ 1064 nm
Diode Laser Glass
Doublets/ LAI
cemented
2 elements:
N-SK11 &
N-SF5
3.8 - 2.5
780 - 1550 nm
60 - 40
< λ/5 @ 830 nm
over CA
Low to medium
power
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Our LAP series visible air-spaced doublets, made from
N-SF11 and optimized for 633 nm, are ideal for use at
visible and near infrared wavelengths. The use of N-SF11
means that these lenses have higher refractive index for
greater focusing power and good transmission throughout
the visible and near infrared. However, this slightly softer
glass is more difficult to polish with premium surface
quality (40 - 20 scratch and dig is specified), and carries
lower damage resistance than fused silica.
The LAPQ series, optimized for 248 nm, is designed to
be used for high energy or UV applications. They are
made from high purity UV-grade fused silica (the “Q”
designates UV-grade fused silica used in place of N-SF11).
Fused silica offers high transmission throughout the UV,
visible and near infrared wavelength regions, excellent
homogeneity and thermal stability, and high damage
threshold. These lenses are also inspected to high surface
quality (10 – 5 scratch and dig), appropriate for high
power applications. Although they see common use as
excimer laser focusing lenses due to their 248 nm design
wavelength, they are also suitable for high energy 1064 nm
Nd:YAG laser beam steering applications. For the highest
damage threshold, we recommend the LAPQ fused silica
aplanat with a narrowband V-coat antireflection coating.
The APM and APMQ series are aplanatic meniscus lenses
used to shorten the focal length of the LAP and LAPQ
laser aplanats without introducing additional coma or
spherical aberration. To do so, the meniscus lens must
be designed to match the spherical wavefront generated
by the preceding aplanatic lens, and it must be properly
spaced relative to its companion aplanat. Therefore
the APM and LAP, and the APMQ and LAPQ lenses are
used in pairs. CVI Laser Optics provides each aplanatic
meniscus lens pre-mounted in a housing to ensure proper
spacing and orientation relative to its paired aplanat.
The use of a meniscus lens provides a combined system
APM/LAP or APMQ/LAPQ with an f number of 3.3 that
maintain optimized beam quality and offer significantly
better performance than would otherwise be achieved
with a single component, especially in systems utilizing
monochromatic light.
The LAI series of lenses are a versatile solution for diode
laser beam focusing and collimation. These aplanatic
cemented doublets offer diffraction-limited performance
when used at single diode laser wavelengths through
the entire near-IR spectrum. They have been corrected
for spherical aberration, coma, astigmatism, and
spherochromatism for use with monochromatic light
at any wavelength from 780 – 1550 nm. Pure chromatic
aberration (variation of focal length with wavelength)
has been left uncorrected to provide greater freedom in
other corrections, since it does not have any significant
effect on the performance of these lenses when used
with diode lasers. The correction of spherochromatism is
achieved using two different materials with complementary
dispersion, N-SK11 and N-SF5. Correction of
spherochromatism is important because it allows LAI
lenses to be used at a wide variety of (monochromatic)
wavelengths by simply adjusting the back focal position to
compensate.
Achromats
Unlike aplanats, achromats are designed for use with
multiple wavelengths. They use a combination of two or
more lens elements of differing materials to compensate
for the inherent dispersion properties of the substrate
materials, and thus minimize the overall variation of
the focal length with wavelength. In a typical positive
achromat, the positive elements are constructed from
a low index (crown) glass, and the negative elements
are constructed from a high index (flint) glass material
with higher dispersion. Achromatic lenses are designed
to correct for chromatic aberration at two distinct
wavelengths (often blue and red) and to minimize spherical
aberrations; other aberrations such as coma may also be
corrected. They can be designed for broad wavelength
ranges (usually visible 400 - 700 nm) or for two distinct
wavelengths (1064 nm & 532 nm for instance). Care
should be taken when operating outside of the design
wavelength range, as performance may change. For
questions regarding selection of achromats, contact a
CVI Laser Optics applications engineer). Also, because
achromats are not symmetric in either design or function,
they will exhibit significant wavefront distortion if not
oriented correctly.
Achromatic doublet and triplet lenses are often cemented,
as this technique produces high durability and mechanical
strength, increased overall transmission as a result of
fewer surface reflections (which are produced by external
surfaces), and precise centration control. However,
low transmitted wavefront distortion is more difficult to
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Acromat Lens Type/
Product Code
Construction
Elements &
Materials
ƒ/#
Wavelength
Range
Surface
Quality
Surface Accuracy
LDT
Laser-Grade Visible
Cemented Achromat/
LAL
cemented
2 elements:
N-BAK4 &
N-SF10
3 - 2.2
415 - 700 nm
20 - 10
< λ/2 (f/# < 3.0)
< λ/4 (f/# ≥ 3.0)
@ 546.1 nm over CA
Low to medium
power
Precision-Grade Visible
Cemented Achromat
AAP/AAN
cemented
2 elements:
N-BK7 & N-SF2
46.3 - 4.6
425 - 675 nm
40 -20
TWD < λ/2 p-v @ 633
nm over CA
Low to medium
power
Standard 400 - 700 nm
Cemented Achromat
LAO
cemented
15.6 - 1.7
2 elements:
N-BAK4, -SF10,
N-BK7,
N-SF5, N-SF8,
N-BAK1, or
N-SK11
400 - 700 nm
60 - 40
< λ/2 (f/# < 3.0)
< λ/4 (f/# ≥ 3.0)
@ 633 nm over CA
Low to medium
power
1064/633 nm Airair-spaced
Spaced Laser Achromat
HAP/HAN
3 elements:
N-BK7 &
N-SF11
5
633 - 1064 nm
40 -20
TWD < λ/2 p-v @ 633
nm over 95% of CA
4 J/cm2, 20 ns, 20
Hz @ 1064 nm
1064/532 nm Airair-spaced
Spaced Laser Achromat
YAP/YAN
3 elements:
N-BK7 &
N-SF11
5
532 nm &
1064 nm
40 -20
TWD < λ/2 p-v @ 633
nm over 95% of CA
4 J/cm2, 20 ns, 20
Hz @ 1064 nm
achieve, and laser damage threshold and power handling
are severely compromised by the cement layer. With
air-spaced achromats, high damage threshold and low
transmitted wavefront distortion through the assembly
can be achieved. As with aplanats, air-spacing the
components also allows for more flexibility in the design
which in turn leads to even better color correction. This
option is nevertheless more expensive because both
sides of the components must be coated to minimize
reflection losses, and extra mechanical parts are required.
Achromats find use in broadband applications, including
astronomical telescopes, color photomicrography, plasma
spectroscopy, and biomedical instrumentation.
Our line of visible achromats includes three grades:
standard, precision, and laser-grade, each suited to
a different type of performance requirement. All are
cemented doublets composed of complementary
crown and flint glasses, computer optimized for infinite
conjugate ratio and suitable for use with low to medium
energy lasers. These achromats have been corrected for
spherical aberration and coma, with the achromatization
constraint slightly relaxed in favor of monochromatic
aberration suppression, resulting in a superior achromatic
lens. (Precise focal length equality at the extreme design
wavelengths is excessive and impairs overall performance.)
These achromats therefore perform much better than a
singlet lens for monochromatic applications at any visible
wavelength.
Due to the superior imaging properties of CVI Laser
Optics’ visible achromats, there is often interest in using
them outside the visible spectrum. When moving from
the mid-visible to 1064 nm, you may observe a 0.5 – 1.0 %
increase in focal length due to the several different glass
combinations utilized in the series. A similar amount of
variation in back focal length (ƒb) and secondary principalpoint position can be expected.
Our LAO series standard 400 – 700 nm cemented
achromats are well-suited to general-purpose imaging
tasks and low-power laser beam manipulation. Surface
accuracy is λ/4 to λ/2 over 90% of the diameter, and
they are inspected to a minimum surface quality of 60-40
scratch and dig. Standard grade lenses are an economical
solution for many applications, but lower surface accuracy
impacts resolution. They are provided with a broadband,
single layer MgF2 antireflection coating for 400 – 700 nm.
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For applications requiring a negative focal length or an
achromat with better surface quality, we recommend
our AAP/AAN series precision grade visible cemented
achromats. These achromats are also manufactured
with better surface accuracy at large diameters, with
transmitted wavefront distortion of ≤ λ/2 over 85% of the
diameter. Constructed using N-BK7 and N-SF2 glass
elements, their surface quality is inspected to 40-20 scratch
and dig, which makes them ideal for reducing scatter and
stray light reflections. These lenses are provided with a
broadband antireflection coating with ≤ 0.5% average
reflectivity for 425 – 675 nm. The AAP/AAN lens series
includes a large selection from stock of larger diameters
(up to 101.8 mm) and longer focal lengths (up to 2.0 m).
They are a moderately-priced solution for many imaging
and low power laser applications.
The LAL series laser grade visible cemented achromats
are specifically designed for laser-beam manipulation and
focusing of low to moderate power laser beams. They
are manufactured to tighter focal length tolerances and
20-10 scratch and dig surface quality for minimal scatter,
spherical aberration and coma. For this reason, they are a
better choice than our LAO lenses for performance-critical
applications, even those at low power. Constructed using
N-BAK4 and N-SF10 glass elements, they are available
with a broadband antireflection coating with ≤ 0.5%
average reflectivity for 415 – 700 nm.
Achromats are also used in dual wavelength beam
steering applications. Alignment of near infrared lasers
and diodes can be much simpler when performed using a
visible HeNe or doubled Nd:YAG laser beam following the
same optical path, in which case any in-line focusing and
collimating lenses need to function equally well at both the
laser and alignment beam wavelengths. Our HAP/HAN
series of laser achromats are air-spaced triplets designed
with the same focal length at 1064 nm and 633 nm for
focusing of Nd:YAG and HeNe laser beams to the same
point. They also have excellent achromatic performance
for Ti:Sapphire laser use at 800 nm. These achromats
can be used to form beam expanders that collimate at
the same lens spacing, and are corrected for spherical
aberration at both wavelengths and for coma at 1064
nm. Our YAP/YAN series of air-spaced laser achromats
perform similarly, operating at 1064 nm and 532 nm for use
with Nd:YAG and its second harmonic. These lenses are
corrected for spherical aberration at both wavelengths,
and for coma at 1064 nm. Each of our laser achromats
have high quality antireflection coatings, which combined
with the air-spaced construction and good cosmetic
surface quality allows them to be used for high power
applications. The low transmitted wavefront distortion (λ/2
@ 633 nm) also makes them ideal for performance-critical
applications.
Our achromats are manufactured to test-plate
specifications to ensure the very best quality. Their
surfaces are checked for power and irregularity during
the lens production process using precision master test
plates, and laser-based interferometers are used to
control the quality of the finished components. Tight
centration tolerances are maintained in all dimensions
to ensure optimum performance and conformance with
their specifications. Focal and principal-point positions
are accurately known and are essentially independent of
f-number when spherical aberration is very well corrected.
Instruments can be designed around these lenses with
confidence that little alignment will be required when the
lenses are installed.
Objective lenses
Objective lenses are achromatic or aplanatic lens systems
with more complex opto-mechanical designs, designed to
operate at lower f/numbers or provide specific corrections.
CVI Laser Optics offers two series of objective lenses with
various numerical apertures for near-UV, visible and nearinfrared applications.
Our GLC objective lenses are designed for collimating
and focusing diode lasers, offering diffraction limited
performance. Two different series are available: one with
a 405 nm design wavelength for use at 395 – 415 nm,
and one with a 830 nm design wavelength for use over
the 633 – 1550 nm wavelength range. They are offered
with a variety of numerical apertures, all having the same
clear aperture, and can be used in pairs to both collimate
and refocus the laser energy to a diffraction limited spot
with different diameters and distances from the diode
laser. These lenses have been corrected for spherical
aberration, coma, astigmatism, and spherochromatism for
use with monochromatic light at any wavelength within
their operating range. It is important to note that they are
not achromatic, but the correction of spherochromatism
allows them to be used at a wide variety of monochromatic
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wavelengths by simply adjusting the back focal position.
In addition to diode lasers, these lenses can be used with
other narrow-band laser sources, or for fiber optic coupling
and collimating.
Our OAS standard microscope objectives are achromatic
within the visible wavelength range, and are designed for a
160 mm tube length with standard RMS mounting thread.
They are “parfocal”, which means that they have the
same distance from the objective mounting flange to the
object, allowing objectives to be easily interchanged with
a minimum of refocusing. Available in numerical apertures
from 0.12 to 0.65, they are also useful for focusing lower
power visible lasers, and for constructing spatial filters and
beam expanders. These objectives are color-corrected
for viewing and visual inspection. When choosing an
objective, keep in mind that an objective with a larger NA
gathers more light and has higher resolution but provides
a smaller depth of field and shorter working distance, and
costs more than an objective with a smaller NA.
F-Theta lenses
Laser scanning systems using galvanometer mirrors or
rotating polygons require special scanning lenses to create
flat (planar) imaging fields. Although standard scanning
lenses provide a flat field, the distance traveled by the
scanned spot is not a linear function of the deflection
angle, requiring the use of complex electronic correction
algorithms within the drive electronics. F-theta lenses
improve on this by adding extra elements and a precise
amount of barrel distortion to the scanning lens, thus
resulting in a spot position that is directly proportional
to the scan angle. Our FTL series of F-theta lenses are
designed for high power use at 1064 nm, and offer a
small and uniform spot size over the entire scan field as
well as exceptionally high scan linearity. These lenses are
ideal for most marking, writing, and photoresist exposure
applications, but may cause angled holes and chamfers
in cutting and drilling applications. Telecentric F-theta
lenses should be used for these critical applications. In
addition to industrial material processing, F-theta lenses
are used in science and research, as well as in medical and
biotechnology applications like confocal microscopy and
ophthalmology.
When selecting an off-the-shelf F-theta scanning lens
or specifying a custom lens, there are many parameters
to consider, the most important being the operating
wavelength, focused spot size, scan field dimension, and
the need for telecentricity. These factors place constraints
on parameters like entrance pupil diameter and location,
as well as deflection angles and focal length selection, and
determine input beam diameter and galvanometer mirror
locations and size. Other parameters to be considered
are the laser damage threshold, front and back working
distance, scan lens size and mounting interface.
Laser beam expanders
Beam expanders are optical systems used to increase
the diameter of a beam, or to decrease it (when used
in reverse). Since the product of beam diameter and
divergence of a laser beam is constant, increasing the
beam diameter will reduce the divergence of the beam by
the same factor. CVI Laser Optics offers several types of
beam expanders, all based on a compact Galilean design
composed of a diverging lens group and a collimating
lens group. The use of a Galilean design has several
advantages: no internal focus, a more compact housing
design, and the design flexibility to have the second lens
group effectively cancel spherical aberrations induced by
the first. As the spacing between the two lens groups is
adjusted, the degree of collimation is varied continuously.
Beam expanders find use in laser communications and
distant target illumination applications. In addition,
because an expanded laser beam can be focused to a
much smaller spot size than an unexpanded one, beam
expanders are also used extensively in light focusing
applications.
Our LBX standard beam expanders are a cost-effective
option for broadband applications using low power visible
lasers. They work well to expand a laser beam for uniform
illumination of a large area, with wavefront distortion of
1λ or less peak to valley at 633 nm. They use a cemented
construction, making them suitable for use only with low to
medium energy lasers.
If working at higher power, or at UV or near infrared
wavelengths, consider one of our high energy beam
expanders. These air-spaced assemblies are manufactured
using high quality UV-grade fused silica bestform lenses.
Fused silica offers superior transmission in the UV,
excellent homogeneity and thermal stability, and higher
damage threshold than N-BK7. All possess a transmitted
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wavefront distortion of λ/2 over 85% of the clear aperture,
and are coated with low loss, high energy AR coatings
at user specified wavelengths. The BXUV series has
been designed for 266 nm, and the HEBX for 1064 nm,
giving options for high power laser use at UV through
NIR wavelengths. We also offer a line of dual wavelength
beam expanders for more demanding applications using
Nd:YAG lasers. The DWBX series includes 1064/532 and
1064/633 nm beam expanders for use in beam alignment
and research. Their Galilean design uses two high power
AR-coated triplet lenses, and are corrected for chromatic
and spherical aberrations at both design wavelengths, as
well as for coma at 1064 nm. With better wavefront quality
and achromatization than telescope objectives, these high
quality beam expanders can be used to simultaneously
expand Nd:YAG and doubled Nd:YAG beams, or to alter
the diameter of a Ti:sapphire laser at 800 nm.
Shear plate collimation testers
A shear plate is a very simple interferometer, using
interference between two wavefronts to generate a fringe
pattern containing information about the wavefront of
the incident beam. Shear plates can be used to adjust
a laser collimation system, measure a wavefront’s radius
of curvature, determine wavefront symmetry, measure
the power of long focal length optics, and in some cases
analyze wavefront aberrations.
Shear plates are thick, high quality optical flats, generally
oriented at 45° to the test beam. Wavefronts reflecting
from the front and back surfaces are said to be “laterally
sheared”, i.e., offset with respect to one another due to
the finite thickness of the plate. Interference occurs in
the region where the wavefronts overlap, as shown in
the diagram. CVI Laser Optics uses high quality wedged
N-BK7 shear plates with λ/20 surface flatness (at 633 nm) to
produce a gradual path difference between the front and
back surface reflections. Consequently, a parallel beam of
light produces a linear fringe pattern where the reflections
overlap. Our SPM shear plate collimation testers use
shear plates mounted in a housing containing a viewing
screen to simplify visualization and measurements of the
fringe pattern.
Fig 4: Shear plate collimation tester
A perfectly collimated beam will produce equally spaced
fringes parallel to the reference line on the viewing screen.
A beam that is reasonably close to collimation will still
produce equally spaced fringes, but they will be rotated
with respect to the reference line. The wavefront radius
of curvature of the beam can be calculated using R =
sδ/(λsinθ), where s is the shear distance, δ is the fringe
spacing, and θ is the angle of rotation relative to the
reference line. For CVI Laser Optics shear plate modules,
a convergent beam will produce a clockwise rotation,
while a divergent beam will produce a counter-clockwise
rotation when viewed on the display screen. If the beam
being tested overfills the viewing screen, it is acceptable
to temporarily reduce the diameter of the beam with an
iris to measure the shear distance, as s is not dependent
on the beam diameter.
Fig 5: Measurable quantities needed in order to use the shear
equation.
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CVI Laser Optics’ line of collimation testers consists of
three sizes. Modules with clear apertures 25, 50 and
85 mm are available. In each case the wedge angle is
chosen such that a collimated 632.8 nm laser beam filling
the entire aperture will display approximately six fringes
across the screen (more fringes will be visible for shorter
wavelengths). A minimum of one fringe is required in the
interference region to adjust the collimation. Since the
size of the interference region is dependent on the shear
distance, CVI Laser Optics shear plates require a minimum
beam diameter of 5, 10 and 15 mm respectively.
To calculate the nominal shear distance, s, for our
collimation testers, the following equation may be used,
where t is the thickness of the optical flat:
Eqn. 11
At θ = 45° and λ = 632.8 nm, for N-BK7 (n=1.518522), this
reduces to:
Eqn. 12
Shear distance for the optical flats offered by CVI Laser
Optics is summarized below:
Collimation
Tester
t (mm)
Shear,
s (mm)
09SPM001
6
4.47
09SPM003
10
7.44
09SPM005
15
11.16
Once the radius of curvature has been calculated from the
fringe pattern, the divergence or convergence of a beam
can then be calculated by dividing the diameter of the
beam (or input aperture of the shear plate, whichever is
smaller) by the calculated radius of curvature.
Using these methods, it is easy to see how a shear plate
can be used as a simple visual detector for adjustment of
a laser collimation system. The high quality of our SPM
shear plate collimation testers can even be used to set
the divergence/convergence of a laser collimating system
to less than 20 µrad. It must be remembered, however,
that the resultant beam is only truly collimated at the
point of measurement, and that the wavefront will acquire
curvature beyond that point. Therefore a shear plate
should only be used to set collimation, and thus locate the
beam waist, at the center of the region of interest.
Use of the SPM collimation testers is not limited only to
visible wavelengths, as N-BK7 provides good transmission
from 350 nm to past 2000 nm. Sensitivity of the eye
decreases rapidly beyond 780 nm, but can be augmented
in the near infrared through the use of viewing devices like
phosphor laser display cards, infrared image converters
and CCD cameras.
Defining the focal length of multielement lenses
CVI Laser Optics uses the following conventions and
nomenclature when describing multielement lenses. As
with a singlet, the back focal length, fb, is the signed
distance from the rear vertex to the back paraxial focal
plane. By signed distance, we refer to the distance noted
with negative or positive value, depending on whether it
is a positive or negative focal length. This is shown in the
figure below for a positive triplet.
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The advantage of a consistent formalism is evident in the
construction of a Galilean beam expander, shown below.
Here, both the negative and positive elements will have a
common focus, as shown.
Fig 6: Definition of back focal length for a positive triple
For a negative lens, ƒb is negative and is calculated using
the same rule. The back focal length is the distance from
the back vertex to the (virtual) back paraxial focal plane.
We have put absolute signs around ƒb in the figure below
to emphasize this.
Fig 8: Back focal lengths in a Galilean beam expander
To determine the spacing of the elements, distances
strictly referenced to optical surfaces are required. The
logical choice is to use the back focal lengths, thus we
have:
d = (ƒb)positive + (ƒb)negative = |(ƒb)positive| − |(ƒb)negative|
Fig 7: Definition of back focal length for a negative lens
Eqn. 13
It may be noted that the equation above is not actually
consistent with our definitions when the direction of the
light rays is considered. Strictly speaking, it is the front
focal distance of the positive element that is required
in the formula above. However, it is customary to list
the back focal length of a lens as the distance from its
last element to the focal plane when the lens is properly
oriented for focusing a collimated beam from left to right.
So, to design a system using lens tabulated values, keep in
mind the orientation conventions used in the descriptions
of the individual component lenses.
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The working distance (WD) of elements in housings is
provided in the product specifications. The working
distance specifies the distance from the focal plane to a
mechanical reference surface; here it is the housing edge
closest to the focal plane. This is shown schematically in
the figure below:
Fig 9: Working distance of elements in housings
Making the final decision
Selecting the right multielement lens or lens assembly
involves identifying and quantifying the degree and
type of aberrations that can be tolerated by the system,
balanced by the wavelength requirements. If working at a
single wavelength or over a narrow range, it is important
to look equally at our achromats, aplanats and objectives
lenses to find the best solution, as each particular series of
lenses offers subtle differences in how achromatization is
balanced vs. spherical aberration and coma correction or
vice versa. Thought should also be given to the required
specifications for the lens assembly. This will depend
on the application, but performance factors to consider
include laser damage threshold, degree of scatter,
wavefront distortion quality, and focal length tolerance.
Most of CVI Laser Optics multielement lens design
prescriptions are available in many of the commercially
available optical design software packages, such as Zemax,
to facilitate computer analysis. If one of our catalog
multielement lenses is unable to fulfill your requirements,
please contact us to discuss a custom solution.
CVI Laser Optics aplanat marking conventions
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Selection Guide
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