How to Select a Spherical Lens

How to Select a Spherical Lens
Lenses are an integral component in most optical systems,
where they are used to focus, collimate, expand, collect
and image light. Many optical tasks require several lenses
in order to achieve an acceptable level of performance.
This selection guide will review the singlet spherical
lens shapes offered by CVI Laser Optics and offer some
practical guidance on determining the best material type
and lens quality for your application. For a complete
discussion of lens theory, use, and aberrations please refer
to the Fundamental Optics and Gaussian Beam Optics
sections of the Technical Guide.
Lens Shape
CVI Laser Optics offers four lens types for converging or
focusing light. A bi-convex lens is the classic symmetric
lens, possessing two convex surfaces of equal radii.
Bi-convex lenses have positive focal lengths and form
both real and virtual images. It is the best singlet lens
for imaging at unit magnification; spherical aberration
is minimized, and coma, distortion, and transverse
chromatic aberration exactly cancel each other out for a
perfectly made lens (longitudinal chromatic aberration
is not corrected). This is true regardless of the material
used or wavelength, although use of a remote stop can
reduce the degree of cancellation. Aberrations increase as
conjugate ratios (object distance/image distance) depart
from unity. Bi-convex lenses can also be used for focusing
applications, in particular when a lower f-number (ƒ /CA) is
required, even if they do not have the best shape for this
conjugation. They are recommended for virtual imaging
of real objects and for positive conjugate image ratios
from approximately 0.2 to 5 (note that these values are
wavelength sensitive).
Away from unity, the singlet lens shape that best minimizes
spherical aberration at a given conjugate ratio is called
a bestform lens, in which the two convex sides are of
different radii. The marginal rays are equally refracted
at each of the lens/air interfaces for this shape, and
surface-reflection loss is minimized. Another benefit
is that absolute coma is nearly minimized for bestform
shape, at both infinite and unit conjugate ratios. It does
Fig 1: Bestform lens
not, however, perform well in wide-field applications,
except in very specific configurations (with a meniscus for
instance). At infinite conjugate ratio, the best form lens
is not the optimum singlet shape, since it results in high
field curvature. Positive bestform lenses are of exceptional
performance and provide the smallest spot size available
in a singlet lens.
When working at infinite or near-infinite conjugate ratio,
plano-convex lenses with the convex side toward the
infinite conjugate perform nearly as well as the best-form
lens. Convex on one side and flat on the other, these
positive focal length lenses cost much less to manufacture
than a bestform lens. This lens shape also exhibits nearminimum transverse spherical aberration and near-zero
coma when used off-axis. Longitudinal aberration is low,
but is only minimized when using a best form lens.
If bulk light collection is required at minimal cost, an
aspheric glass condenser lens may be the solution.
Aspheric lenses provide better performance by reducing
aberrations when used in low f-number, high-throughput
applications. One surface is aspheric; the second surface
is flat, or spherical-convex. A flat second surface minimizes
aberration, while a spherical-convex second surface
provides the lowest f-number and highest transmission.
Only single-layer MgF2 antireflection coatings are
recommended for these lenses due to the steep curvature
of the surface. The molding and felt-polishing processes
used to manufacture these lenses economically, together
with the use of optical crown glass, makes these lenses
best suited to less demanding light collection applications.
They are not recommended for imaging, precise focusing,
or high power applications, but are ideal for gathering
low-power light with minimal aberration.
CVI Laser Optics offers two lens types for diverging or
expanding light. A bi-concave lens is a symmetric lens,
possessing two concave surfaces of equal radii. Biconcave lenses have negative focal lengths and form only
virtual images which can be seen through a lens. They are
used in laser beam expanders, optical character readers,
viewers, and projection systems to diverge collimated
incident light.
Like their convex counterparts, plano-concave lenses can
reduce aberrations as compared to bi-concave lenses,
depending on the configuration. They have a negative
focal length and are often used to expand light or to
increase focal lengths in optical systems, as they diverge
collimated incident light. When working at infinite or nearinfinite conjugate ratio, plano-concave lenses with concave
side toward the infinite conjugate reduce spherical
aberration, and coma. Additionally, the negative spherical
and chromatic aberration that plano-concave lenses
exhibit can be used to balance the aberrations resulting
from other lenses within a system.
Fig 2: Plano-convex lens
Fig 3: Aspheric glass condenser
Lens Materials
Aside from lens shape, the material a lens is made from
has the greatest impact on its performance. Not only does
it determine the transmission properties, refractive index,
laser damage threshold, thermal coefficient, durability and
weight, but it also impacts cost. It even imposes practical
limits on manufacturing tolerances, especially surface
cosmetic quality. CVI Laser Optics utilizes six different
materials to manufacture our catalog singlet lenses, but
other materials such as magnesium fluoride, sapphire,
germanium, and Suprasil are available on a custom basis.
We can also manufacture many of our lenses with custom
dimensions and focal lengths.
Fig 4: Bi-concave lens
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particularly at larger diameters. ArF grade fused silica for
use at 193 nm is also available upon request.
N-SF11 is a type of lead- and arsenic-free Schott glass
with much higher refractive index than N-BK7, resulting in
greater focusing power and reduced spherical aberration.
Its transmission is best in the visible and near-infrared,
from 500 nm – 2.5 μm. Though its thermal characteristics
are similar to N-BK7, it is a slightly softer glass, resulting
in lenses with lower surface quality than their N-BK7
Fig 5: Plano-concave lens
N-BK7 is a lead- and arsenic-free borosilicate crown glass
that is used widely in the optics industry. It has excellent
transmission from 350 nm – 2.0 μm, good thermal
expansion coefficient, moderate laser damage threshold,
and is relatively low in cost. It is a hard glass that stands
up well to handling, with good chemical resistance.
Our fused silica is Corning 7980 UV-grade, a synthetic
form of fused silica manufactured by flame hydrolysis to
extremely high standards. Its ultra-low impurity content is
evident in the wide transmission range of 180 nm – 2 μm
and its high laser damage threshold. It does not fluoresce
in response to wavelengths longer than 290 nm, and in
general exhibits good resistance to radiation darkening
from ultraviolet, x-rays, gamma rays, and neutrons. It also
boasts excellent thermal properties, including a wide
operating temperature range, low thermal coefficient,
and resistance to thermal shock. Fused silica lenses from
CVI Laser Optics have increased hardness and resistance
to scratching, resulting in better surface quality than their
N-BK7 equivalents.
Excimer grade fused silica is UV-grade fused silica that
has been manufactured with near-zero defects for use with
high power KrF lasers at 248 nm. This material has very
low levels of inclusions, bubbles, striation and striae, and
minimal variations in index of refraction. Its exhibits the
lowest level of laser induced fluorescence of all the Schott
glasses, strong resistance to radiation-induced defect
generation, and higher UV laser damage threshold than
CaF2. It is one of the more expensive UV material options,
CaF2 is a cubic single-crystal material with transmission
spanning the deep UV through infrared, 150 nm – 8 μm. It
can be mined or manufactured synthetically, but is higher
in cost than other lens materials, particularly in the highpurity forms used for deep-UV applications. That being
said, its excellent transmission and high laser damage
threshold in the deep UV makes it the material of choice
for many excimer laser applications. Lenses manufactured
with CaF2 tend to have slightly lower surface quality than
their N-BK7 or fused silica equivalents.
Optical crown glass is a low-index, commercial-grade
glass. Its index of refraction, transmittance, and
homogeneity are not controlled as carefully as in opticalgrade glasses like N-BK7. It transmits from 200 nm – 2
μm, with best performance from 400 nm – 1.5 μm. Though
its thermal expansion coefficient is reasonable and its
hardness makes it robust to handling, its laser damage
threshold is low.
Lens Quality
Once the lens shape and material has been selected, the
next step is to determine the lens quality required. This
will depend on the application and performance needed,
but factors to consider include laser damage threshold,
degree of scatter, surface figure, and focal length
Standard lenses possess a surface irregularity of λ/4 to
λ/2 before coating, and are manufactured to a minimum
surface quality of 60-40 to 40-20 scratch and dig,
depending on material. They are an economical solution
for many applications, but lower surface accuracy impacts
resolution, and laser damage threshold is not as high.
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CVI Laser Optics offers standard singlet lenses in both
N-BK7 and fused silica. These lenses are available
uncoated, or with a selection of antireflection coating
options from the UV to near-infrared.
Our laser quality lenses differ from standard lenses in
two key aspects. First, high cosmetic surface quality
(10-5 scratch and dig for fused silica, 20-10 for CaF2 and
N-SF11) reduces scatter, making them more suitable
for high energy laser applications. Second, careful
polishing to λ/10 surface figure and tighter paraxial focal
length tolerance yields the low wavefront distortion and
accuracy required for use in ultra-violet and performancecritical applications. The term “laser quality” therefore
refers to both high laser damage threshold and to high
performance specifications. CVI Laser Optics manufactures
CaF2, N-SF11, and excimer grade UV fused silica spherical
lenses only in laser quality grade. All of our laser quality
lenses are available with a wide range of broadband,
dualband 1064/532, and narrowband V-coat antireflection
coatings at wavelengths from the UV through nearinfrared. These AR coatings offer high durability and
damage threshold, low loss, and peak performance
when applied to laser quality optics. For best laser
damage threshold performance, we recommend V-coat
antireflection coatings on laser quality 10-5 fused silica
Our aspheric glass condenser lenses, in contrast, are
fabricated to light collection quality standards. This
involves a low-cost process in which the aspheric side is
precision molded and the second surface is felt polished
to achieve 80-50 scratch and dig surface quality. Light
collection quality is more than adequate for many low
f-number, high throughput applications in the visible
wavelength region, and provides an economical alternative
to standard N-BK7 lenses. These lenses are available with
an optional single-layer MgF2 coating for 400 – 700 nm.
Making the final decision
Choosing the right singlet lens or combination of
lenses for your application involves much more than
identifying the required lens material and quality. Detailed
performance analysis of an optical system is accomplished
by using computerized ray-tracing software, and CVI Laser
Optics applications engineers are available to provide a
ray-tracing analysis of simple catalog-component systems.
If you need assistance in determining the performance of
your optical system, or in selecting optimum components
for your particular application, please contact us.
Numerous other factors, such as lens manufacturing
tolerances and component alignment, impact the
performance of an optical system. It should be kept in
mind that if calculations indicate that a lens system only
just meets the desired performance criteria, in practice
it may fall short of this performance as a result of other
factors. In critical applications, it is generally better to
select a lens whose calculated performance is significantly
better than needed.
In addition to the array of singlet lenses described,
CVI Laser Optics also offers many cylindrical lenses,
as well as multi-element lenses that can simplify your
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optical design. No singlet lens can correct for chromatic
aberration, an important consideration when working
with multiple wavelengths. Achromatic lenses may be
needed to improve performance in this case. Additionally,
a multielement lens system is often required at low focal
ratios when the aberrations of a singlet lens are too large
to satisfy performance requirements. Regardless of your
needs, we can work with you to find the right solution
by combining products from our catalog with lenses
manufactured to your exact specifications using custom
Selection Guide:
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