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Diffractive Optics Are Not Just Lenses
By Kurt Kanzler - Diffractive Laser Solutions
I.
Introduction
Diffractive optical elements ( DOEs ) are valuable components that enhance
a full spectrum of commercial systems. Companies that use DOEs are making
optical systems with fewer elements at lower cost. As design engineers
look to new system layouts, DOEs are being considered for their unique
properties. The mix of single wavelength laser sources with highly efficient
DOEs can produce very interesting, useful, high quality results.
II. Applications of DOEs
1. Beam steering is the simplest application of DOEs. A linear phase grating with a given period can be used to steer a beam through an optical system. Depending on the wavelength, a DOE can steer a beam at angles as high as 60 degrees.
2. Beam sampling is a useful application for a linear phase grating. A low power pick-off from a laser beam can be used to monitor real-time power and beam quality while a laser is doing some work.
3.
A Dammann grating will produce several output beams from a single input
beam. This application can simulate multiple sources and can be used
for various jobs.
4. Spherical aberration can be corrected by the use of a phase grating
placed on the surface of a refractive lens.
5. Chromatic correction is an application of the phase Fresnel lens.
A single hybrid element can chromatically correct over a large bandwidth.
6. Beam profile conversion is an application that employs the use of
a phase lens. A gaussian-to-tophat beam converter is a specific application
where DOEs typically outperform all other method.
7. A complex phase grating can be used as a irradience profile shaper
to produce various geometric shapes. Company logos and other text based
outputs can be easily produced with a single DOE.
III. Unique Features of DOEs
One unique feature of DOEs is their high dispersion characteristics.
This property allows for chromatic correction of traditional refractive
optics. If a wedged piece of ZnSe is used to steer a .633 um laser beam
at an angle of 0.4 degrees, that same optic would steer a 10.6 um laser
beam at an angle of 0.37 degrees. The usefulness of a grating to chromatically
correct a refractive optic lies in the fact that a grating has negative
dispersion. Most refractive materials have positive dispersion. The
amount of dispersion is apparent in the difference between the refractive
angle and the diffractive angle at 10.6 um. The grating increases the
angular deviation of the refractive wedge by a factor of 187 times in
the opposite direction. Phase gratings are used by many companies to
correct chromatic aberrations in FLIR systems. As the manufacturing
processes of DOEs mature, visible imaging systems will likely see the
use of DOEs for chromatic correction.
Another unique feature of DOEs is their ability to obtain wavelength
scale aperture control. By pixelating the aperture on the scale of several
wavelengths of light, DOEs can produce diffraction patterns that a standard
refractive optic could never obtain. DOEs can produce shaped irradience
patterns that can be tailored to many specific applications. This precision
aperture control allows for the superposition of many different gratings
that all work together to produce a single diffraction pattern. Any
type of geometric shaped diffraction pattern can be produced by a single
DOE surface.
A final unique feature of DOEs is their ability to accommodate harmonic
wavelengths with a single surface. Multiple Order Diffractive1 ( MOD
) optics can be used at several harmonic wavelengths simultaneously
with comparable functionality at these wavelengths. These MOD optics
have some limitations for broadband optical system, however, for laser
based system with several discrete wavelengths, they can perform achromatically.
IV. Grating Theory
All DOEs are gratings. This makes them unique optical elements. A grating
uses the concept of periodicity to produce a diffraction pattern when
light is incident upon it. Any structure that repeats itself perpendicular
to the optical axis is considered a period. Even a single repetition
of a structure will produce noticeable diffraction effects., i.e. an
aperture. The most useful equation for understanding a DOE is the general
grating :
Sin (theta) - Sin (theta)o = m (lambda) / d where (theta) is the incident
angle of light,
(theta)o is the diffraction angle of the m order,
(lambda) is the wavelength incident on the grating,
and d is the period of the grating at the point
of interest.
At
normal incidence, the Sin (theta) term goes to zero, and the equation simplifies
further. Most of the commercial DOEs available currently use the 1st
order, where m = 1 in the above equation.
This simple equation can produce some very interesting results. If we
hold the period d constant in one dimension across the aperture, we
have a linear phase grating that can be used to steer an incoming beam.
If we allow the period to vary from center to edge as some function
of the desired focal length and wavelength, we have a phase Fresnel
lens. If we superimpose several gratings with different periods in one
dimension across an aperture we produce a Dammann grating that splits
the incoming beam into several outgoing beams.
If we superimpose hundreds of gratings with different periods in two
dimensions, we can produce complex shapes from any incoming beam. This
superposition of hundreds of gratings becomes computationally intensive
and makes it apparent that a powerful computer must be used to design
these complex extended imagers2. An extended imager
produces a geometrically shaped intensity pattern that can be projected
for long distances. Even in these complex DOEs, the basic principle
of the simple periodic grating remains.
V. Background History
Diffractive optics have been around for at least two centuries. As far
back as the late 1700s, scientists were reporting on diffraction effects
from various types of amplitude gratings. An amplitude grating blocks
out some portion of the incident light to produce a diffraction pattern.
The throughput of an amplitude grating is some fraction of the incoming
light. Typically 50 % of the incoming light transmits though an amplitude
grating. These early gratings were limited to linear designs. Then,
in the early 1800s, people wanted to use amplitude gratings to focus
light. The Fresnel Zone Plate was born. The Fresnel Zone Plate used
a radial grating design, and had a maximum of 10 % of it's input energy
arriving at the focal point. The amplitude grating's widespread use
was limited by the small amount of transmitted energy. Later, towards
the end of the 1800s, the first functional phase grating was produced.
A phase grating induces a phase delay at certain points in the aperture
by varying the optical thickness at these points. This discovery was
a major improvement over the amplitude grating, since 100% of the incoming
light was transmitted through the phase grating. The stage was finally
set for the development of the modern day Diffractive Optical Element.
The first development which led us to a useful DOE was the concept of
blazing. Blazing minimizes the tendency for a DOE to produce two identical,
symmetric irradience patterns. A DOE with a blazed zone can manipulate
100 % of the incoming light into one single irradience pattern. One
of the early experiments to demonstrate the potential of DOEs was performed
by a group at IBM3. In 1969 the group at IBM built some kinoform (smooth
surface profile) DOEs that used the power of the modern computer as
the design engine. IBM reported interesting results that expanded the
technical communities understanding of the use of gratings. The next
development came a year later, when Dammann4 proposed the idea of a
stepped approximation to the kinoform. In the twenty years that followed,
researchers in the field of optics used this concept of discrete steps
to produce DOEs of all types. A major initiative to commercialize DOEs
was made by MIT in the 1980s. By 1990, optics companies were taking
notice and began producing DOEs for the commercial market.
VI. Misconceptions about DOEs
1.
Comparison to refractive lenses:
A refractive lens varies the thickness of material across the aperture
to obtain a focus. In a refractive lens, 100 % of the transmitted energy
is used to construct an image. Typically, 1st order diffraction efficiency
is compared to the transmitted efficiency of a refractive lens. The
1st order efficiency of a modern DOE may be as high as 99% at a single
wavelength, yet within the framework of direct comparison, a DOE always
seems to fall short. This comparison may be useful since DOEs can be
used as functional lenses. However, this comparison can also be rather
dangerous, because it always shows the DOE coming up short.
If a DOE is not even as efficient as a conventional refractive lens,
then why are manufacturers producing tens of thousands of DOEs per year.
What is really going on here? There is a question of throughput, not
necessarily 1st order efficiency. The amplitude grating is arguably
a poor optical element since it blocks some portion of the incoming
energy. On the other hand, a phase grating transmits all of the incoming
light and therefore is identical in throughput to a conventional refractive
lens. The real value of a DOE in an optical system is defined by the
unique properties of a grating.
2.
Wavelength dependence on 1st order efficiency:
If we limit our discussion to periods that are larger than approximately
10 l, we can use scalar theory to predict 1st order efficiency. For
a typical DOE , 1st order efficiency is dependent on several factors.
However, all of the factors except grating depth are wavelength independent.
You can make a 100 um period linear phase grating with certain manufacturing
tolerance that produces a 97% 1st order efficient phase grating at 10.6
um. That same 100 um period phase grating with the grating depth re-optimized
for .633 um will be 97 % efficient in 1st order for .633 um. Even though
the .633 um wavelength is close to 17 times shorter than the 10.6 um,
the 1st order efficiency is the same. The only difference in performance
for the two 100 um phase gratings would be that at 10.6 um the 1st order
angle would be about 6 degrees , whereas, at .633 um, the 1st order
angle would be about 0.4 degrees.
VII. Conclusion
The use of a DOE as a traditional lens can improve some optical systems. However, the real value of DOEs for optical designers comes from the properties of a grating. If we narrow the scope of DOEs to traditional lenses, we limit the value of DOEs in optical systems. By opening our eyes to the many interesting properties of gratings, the modern optical designer can add a new component to the list of optics to chose for a design. This new degree of freedom has already paid off for many commercial optics companies.
References
1.
G. Michael Morris and Dean Faklis, " Achromatic and Apochromatic
Diffractive Singlets", OSA, JMC4, 1994 Technical Digest series
Vol 11
2. Daniel M Brown and Eric G. Johnson, " More flexible basis set
for DOE lens design" , SPIE-San Jose, 1995
3. L.B. Lesem, P.M. Hirsch, and J.A. Jordan, Jr., " The Kinoform:
A New Wavefront Reconstruction Device", IBM Journal of R &
D - Vol 13(2), March 1969
4. H. Dammann, " Blazed Synthetic Phase-Only Holograms " ,
Optik Vol 31(1), 1970
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