Optical System Design.pdf

Source: Optical System Design

CHAPTER

Basic Optics and

Optical System

Specifications

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Basic Optics and Optical System Specifications

Chapter 1

This chapter will discuss what a lens or mirror system does and how

we specify an optical system. You will find that properly and completely

specifying a lens system early in the design cycle is an imperative ingre-

dient required to design a good system.

The Purpose of an Imaging Optical

System

The purpose of virtually all image-forming optical systems is to resolve

a specified minimum-sized object over a desired field of view. The field

of view is expressed as the spatial or angular extent in object space, and

the minimum-sized object is the smallest resolution element which is

required to identify or otherwise understand the image. The word “spa-

tial” as used here simply refers to the linear extent of the field of view in

the plane of the object. The field of view can be expressed as an angle

or alternatively as a lateral size at a specified distance. For example, the

field of view might be expressed as 10

350

7 matrix of dots will do

just fine. This applies to telescopes, microscopes, infrared systems, camera

lenses, and any other form of image-forming optics. The generally

accepted guideline is that approximately three resolution elements or 1.5

line pairs over the object’s spatial extent are required to acquire an

object. Approximately eight resolution elements or four line pairs are

required to recognize the object and 14 resolution elements or seven line

pairs are required to identify the object.

There is an important rule of thumb, which says that this smallest

desired resolution element should be matched in size to the minimum

detector element or pixel in a pixelated charged-coupled device (CCD) or

complementary metal-oxide semiconductor (CMOS)–type sensor. While

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10°, or alternatively as 350

m at a distance of 2 km, both of which mean the same thing.

A good example of a resolution element is the dot pattern in a dot

matrix printer. The capital letter E has three horizontal bars, and hence

five vertical resolution elements are required to resolve the letter. Hori-

zontally, we would require three resolution elements. Thus, the mini-

mum number of resolution elements required to resolve capital letters is

in the vicinity of five vertical by three horizontal. Figure 1.1 is an exam-

ple of this. Note that the capital letter B and the number 8 cannot be

distinguished in a 3

5 matrix, and the 5

Basic Optics and Optical System Specifications

Figure 1.1

Illustration of Num-

ber of Resolution Ele-

ments Required to

Resolve or Distin-

guish Alphanumerics

not rigorous, this is an excellent guideline to follow for an optimum

match between the optics and the sensor. This will become especially

clear when we learn about the Nyquist Frequency in Chap. 21, where we

show a digital camera design example. In addition, the aperture of the

system and transmittance of the optics must be sufficient for the desired

sensitivity of the sensor or detector. The detector can be the human eye,

a CCD chip, or film in your 35-mm camera. If we do not have enough

photons to record the imagery, then what good is the imagery?

The preceding parameters relate to the optical system performance. In

addition, the design form or configuration of the optical system must be

capable of meeting this required level of performance. For example,

most of us will agree that we simply cannot use a single magnifying

glass element to perform optical microlithography where submicron

line-width imagery is required, or even lenses designed for 35-mm pho-

tography for that matter. The form or configuration of the system

includes the number of lens or mirror elements along with their relative

position and shape within the system. We discuss design configurations

in Chap. 8 in detail.

Furthermore, we often encounter special requirements, such as cold

stop efficiency, in infrared systems, scanning systems, and others. These

will be addressed later in this book.

Finally, the system design must be producible, meet defined packag-

ing and environmental requirements, weight and cost guidelines, and sat-

isfy other system specifications.

How to Specify Your Optical

System: Basic Parameters

Consider the lens shown in Fig. 1.2 where light from infinity enters the

lens over its clear aperture diameter. If we follow the solid ray, we see that

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Basic Optics and Optical System Specifications

Chapter 1

Figure 1.2

Typical Specifications

it is redirected by each of the lens element groups and components

until it comes to focus at the image. If we now extend this ray backwards

from the image towards the front of the system as if it were not bent or

refracted by the lens groups, it intersects the entering ray at a distance

from the image called the focal length. The final imaging cone reaching

the image at its center is defined by its ƒ / numb er or ƒ / #, where

ƒ/number

fo c a l l e n g t h

clear aperture diameter

You may come across two other similar terms, effective focal length and

equivalent focal length, both of which are often abbreviated EFL. The effec-

tive focal length is simply the focal length of a lens or a group of lenses.

Equivalent focal length is very much the same; it is the overall focal

length of a group of lens elements, some or all of which may be separat-

ed from one another.

The lens is used over a full field of view, which is expressed as an

angle, or alternatively as a linear distance on the object plane. It is

important to express the total or full field of view rather than a subset

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Basic Optics and Optical System Specifications

5 aspect ratio. We could specify the horizontal field of

view, which is often done in video technology and cinematography.

However, if we do this, we would be ignoring the full diagonal of the

field of view. If you do specify a field of view less than the full or

total field, you absolutely must indicate this. For example, it is quite

appropriate to specify the field of view as ±10°. This means, of course,

that the total or full diagonal field of view is 20°. Above all, do not sim-

ply say “field of view 10°” as the designer will be forced to guess what

you really mean!

System specifications should include a defined spectral range or wave-

length band over which the system will be used. A visible system, for

example, generally covers the spectral range from approximately 450 nm

to 650 nm. It is important to specify from three to five specific wave-

lengths and their corresponding relative weights or importance factors

for each wavelength. If your sensor has little sensitivity, say, in the blue,

then the image quality or performance of the optics can be more

degraded in the blue without perceptible performance degradation. In

effect, the spectral weights represent an importance factor across the

wavelength band where the sensor is responsive. If we have a net spec-

tral sensitivity curve, as in Fig. 1.3, we first select five representative wave-

lengths distributed over the band,

650 nm, as

shown. The circular data points represent the relative sensitivity at the

specific wavelengths, and the relative weights are now the normalized

area or integral within each band from band 1 through band 5, respec-

tively. Note that the weights are not the ordinate of the curve at each

wavelength as you might first expect but rather the integral within each

band. Table 1.1 shows the data for this example.

Even if your spectral band is narrow, you must work with its band-

width and derive the relative weightings. You may find some cases where

you think the spectral characteristics suggest a monochromatic situa-

tion but in reality, there is a finite bandwidth. Pressure-broadened spec-

tral lines emitted by high-pressure arc lamps exhibit this characteristic.

Designing such a system monochromatically could produce a disastrous

result. In most cases, laser-based systems only need to be designed at the

specific laser wavelength.

Sys tem packaging constraints are important to set at the outset of a

design effort, if at all possible. These include length, diameter, weight, dis-

tance or clearance from the last surface to the image, location and space

450 nm through

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of the field of view. This is an extremely critical point to remember.

For example, assume we have a CCD camera lens covering a sensor

with a 3

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