tutorial

Informations

• Publié par: Erdau
• Nombre de lectures: 33
• Langue: English

Extrait

tutorial
ENGINEERING AN
OPTICAL SYSTEM
Choosing the right starting
point opens up a world of designs.
ILLUSTRATION BY GEORGE ABE
By Warren Smith, Kaiser Electro-Optics
esigning the basic format for an optical almost always done using the thin-lens concept.
system is a process very different from A thin lens has a thickness of zero, an obviousD lens design. It involves determining the impossibility but a very valuable simplification
components of the system and their locations in of the process because a thin component of a
order to produce a system that will meet a set of system can be represented simply by a power
required characteristics. It is the layout of the sys- and a location. Both principal planes in a thin
tem up to, but not including, the lens-design lens are coincident with the lens. The thin lens
stage (in which the lens designer determines the is a concept, not a reality. The lenses are later
detailed component configurations that are expanded to match real components with physi-
needed to do the job.) cal thickness.
The initial layout of an optical system is
july 2002 spie’s oemagazine 49|step by step as a checklist:
The first step in the process should always be to establish the • The purpose of the system (obvious but often overlooked).
requirements and specifications. One should try to collect all • Wavelength, bandwidth, spectral response, or distribution.
of the specifications before beginning the design. The follow- • Aperture diameter.
ing, which will probably be included in a typical set, can serve • Focal length, or magnifying power if afocal. Magnification
and track length if the conjugates are both finite. For finite
conjugates the track length (object-to-image distance) and mag-
nification are sufficient; a focal length specification is
redundant and may constrain the final lens design.
• Numerical aperture (NA) or f-number (f/#). This may be
the infinity f/#, or NA, or the “working” f/#, but it should be
so defined.
• Object size and distance, image size, angular fields of view,
image orientation.=
• Performance: resolution, modulation transfer function
(MTF) at prescribed spatial frequencies, radial energy distribu-
tion, encircled or ensquared energy.
• Sensor characteristics: dimensions, spectral response, pixel
size and number, the aerial image modulation (AIM) curve of the
sensor, system type (visual, photographic, projection, laser, etc).
Figure 1 In this set of MTF curves, the best possible • Physical requirements: spatial limitations, size and location
image contrast for an ordinary optical system is shown in of entrance and exit pupils, cold stop, glare (Lyot) stop, bends
curve A. Curves B through F show the image contrast for or folds needed.
systems with wavefront deformations of λ/4, λ/2, 3λ/4, λ, • Ambient conditions.
and 2λ A system with a quarter wave deformation is often • Thermal stability requirements.
called diffraction limited. • Illumination and vignetting.
Once you’ve assembled this list, the second step, and an
important one, is to question or challenge the specifications.
(b) (a)
(a) (b)
DB
F D
B
F
(b)
(a)
(a) (b)
F
DB DF
B
(b) (a)
(a) (b)
D B (-)F D (-F)
B
Figure 2 Two-component lens systems include (a) telephoto, (b) retrofocus, and (c)
relay, in which a negative focal length provides an erect image. The mirror equivalents
are (a) Cassegrain, (b) Schwarszchild, and (c) Gregorian.
50 spie’s oemagazine july 2002| Are they really necessary? Can the tough ones be eased? Has the about one minute of arc; performance falls off as scene bright-
bar been set higher than necessary, just to be safe? ness decreases. Thus the resolution limit imposed by the eye on
The third step is to ascertain that the specifications are self- the eye-telescope combination is one minute divided by the
consistent. In an afocal system, for example, the magnifying telescope magnification. Remember, although the final perfor-
power must equal the beam expansion factor, the ratio of mance of any system will be largely determined by the quality
apparent field to real field, and the ratio of entrance-pupil to of the lens design, at this point we are only concerned with the
exit-pupil diameter. In a telescope, the eye-lens diameter is limits imposed on the system by general layout.
determined by the eye relief The magnification of a
and the apparent field. In a magnifier or a compoundD B fa fb sum of abs
finite conjugate system, the microscope is, by conven-powers
magnification equals the tion, given as 10 in. divided
0.1 0.7 +0.333 -0.35 5.857ratio of image distance to by its focal length f in inches.
0.2 0.6 +0.5 -0.6 3.667object distance, and it also This convention assumes a
0.3 0.5 +0.6 -0.75 3.0equals the ratio of object side comparison with the object
0.4 0.4 +0.667 -0.8 2.75NA to image side NA (or viewed from a distance of 10
0.5 0.3 +0.714 -0.75 2.733image side f/# to object side in. Under circumstances in
0.6 0.2 +0.75 -0.6 3.0f/#). Check to be sure that which one wishes to obtain
your system requirements 0.1 0.7 +0.778 -0.35 4.143 magnification as a compari-
don’t contradict one another. son with the view from some
Next, resolve any incon- other distance, for example
gruities. Compare the performance specs with known limits to D, the magnification factor is simply D/f. A positive magnifica-
determine whether they are reasonable. The Rayleigh limit for tion produces an erect image; a negative magnification, as in a
point resolution of a perfect lens is 0.61(λ)/NA; the Sparrow compound microscope, indicates an inverted image.
and line resolution limits are 0.5(λ)/NA. For an infinitely dis-
tant object, the Rayleigh angular resolution limit is 1.22(λ)/D getting specific
radians, where D is the entrance-pupil diameter, and (λ) is the An optical system usually falls into one of the following
wavelength. For a visual system, the Rayleigh resolution limit categories:
in seconds of arc equals 5.5 divided by the pupil diameter in • Single component
inches; for the Sparrow limit use 4.5/D. • Two-component (telephoto, retrofocus, relay, etc.)
The MTF cut-off frequency is 2NA/(λ), or 1/(λ)(f/#). In the • Afocal (e.g. telescope)
visible region, the cut-off frequency is about 1800/(f/#) lines • Afocal plus a prime lens
per millimeter. Plotting the MTF, or image contrast, against • Afocal plus a scanner
spatial frequency shows how varying the optical path difference • Periscope (relay, fiber optics, grin rod)
can affect a system’s imaging capabilities (figure 1). Under • Three (or more) component.
ideal, bright conditions, the resolution of the human eye is
cover to cover, reviewed my class notes, and proceeded
designer by default to learn by making mistakes and asking questions of my
betters,” he says.
didn’t want to be an optical designer,” says Warren Years later, Smith was invited to write a couple of chap-
I Smith, chief scientist and consultant for Kaiser Electro- ters for a handbook on military IR technology. “I hemmed
Optics (Carlsbad, CA). “When I took the lens-design and hawed, but eventually I agreed,” says Smith. Those
course at the University of Rochester, I didn’t even buy chapters led to McGraw-Hill asking him to write an entire
the textbook.” Yet today, Smith is the author of Modern book on optical design. But Smith took some convincing.
Optical Engineering, a fundamental text in optical design. “Then they came back and mentioned money, and I
When he graduated in the early 1940s, he found him- couldn’t refuse,” he says with a laugh.
self as part of a top-secret project in Oak Ridge, TN. “At The rest, as they say, is history. “It turns out that the
the time, all I was told was that this was the most impor- approach I took at the time and the development of the
tant thing I could do for the war effort,” says Smith. It field were all very fortuitous,” says Smith. Originally pub-
wasn’t until a couple of weeks later that he realized he lished in 1966, Modern Optical Engineering is in its third
was part of the project to build an atomic bomb, develop- edition. Smith also wrote Modern Lens Design and a sys-
ing equipment to separate U235 from U238 by mass tems layout book. “All told, I guess the books add up to
spectrograph. about 50,000 copies sold,” says Smith. In addition, he has
Smith got into lens designing after World War II, when authored more than 34 papers, holds five patents, and
he went to work for an optical manufacturer in Chicago. “I serves as an expert witness in patent cases.
went out and bought a copy of Conrady, [the textbook he “But the book is my prized accomplishment,” he says.
was supposed to buy for his course], read it three times —Laurie Ann Toupin
july 2002 spie’s oemagazine 51|Single component most widely used in all system layout work. Note that for mir-
The single-component system is simple because it is completely ror systems the mirror radius is simply twice the component
defined by its focal length, aperture, magnification, and field of focal length; a concave mirror has a positive focal length; a con-
view. With an object at infinity, the magnification is zero, but vex mirror, negative.
the image size is the focal length times the angle subtended by There are several widely known special configurations for the
the object. two-component system. If the focal length F is positive and
longer than the overall system length (D+B), t