ENE 492Fundamental of Optical Engineering

Lecture 3

Aberration happens when the rays do not converge to a point where it should be. We may distinguish the aberrations into 6 categories:

◦ Spherical aberration◦ Coma◦ Oblique astigmatism◦ Curvature of field◦ Distortion◦ Chromatic aberration

Lens Aberrations

Rays near axis come to focus at a different distance than marginal rays.

In other words, rays that pass through a lens further away from the optical axis come to a focus closer to the lens than paraxial rays.

Spherical Aberration

Spherical Aberration

This spherical aberration can not be completely corrected with a simple lens.

Complete elimination of this aberration can be done by using a compound lens.

Spherical Aberration

This happens due to various wavelengths in light rays.

The index of refraction varies as a function of wavelength.

A single lens has different focal lengths for different colors.

Chromatic Aberration

Chromatic aberration can be corrected by using two lenses in contact, one made of crown and the other of flint.

Chromatic Aberration

A plane mirror reflects the light without focusing it.

The virtual image formed by a plane mirror is located at the same distance behind the mirror as the object is in front of it.

Mirrors

Mirrors

Assume θ << 1

Mirrors

2

2

2 2

cos 12

11 for 1

1

12cos 2 2

1 12 2 2 2

RIf 0, f = ==>

2

a aa

R R

R Rf R

h

R

For h = 10 cm., R = 2m. Find f.

Example

Incident beam travels left to right, reflected light travels right to left.

Distance is measured from plane of mirror.

Object is on the left of a mirror, then object distance s < 0.

Image to the left of a mirror, then object distance s’>0 (virtual image). Image to the right of a mirror, then image distance s’< 0 (real image).

Mirror Conventions

For converging mirror, focal length f > 0.

For diverging mirror, focal length f < 0.

Mirror Conventions

Example

Example

Think of the last time you viewed yourself in a mirror.(a) Assuming that the mirror surface is perfectly

flat, what are its radius of curvature and its focal length?

(b) Is the image formed by the mirror real or virtual?

Example

The simplest type of camera is the pinhole camera.

The sharpness of the image depends on the diameter of the hole.

If it is too large, the image is blurred.

Thus, as the pinhole is small, the image improves in clarity until a certain pinhole size.

Camera

The advantage of a pinhole camera apart from its simplicity is that all objects are in focus on the screen.

The depth of field of the camera is unlimited.

The disadvantage of pinhole camera is that it admits limited light, so that it is not suitable in freezing the action of moving objects.

Some put a converging lens to improve the brightness and sharpness of the image.

Camera

The aperture, which admits light to the film, is variable and coordinated with the exposure time (shutter speed).

The light power incident at the image plane is expressed as

Camera

2

2

area of aperature

area of image

where D = diameter of aperture

d = diameter fo image

e

DE

d

A lens of f = 4 cm is stopped down to an aperture of 0.5 cm (D). What is the relative aperture or f-number?

Example

From the figure above, the depth of field is (s2 – s1) that may be expressed as

Camera

20 0

2 1 4 2 2 20

2 ( )

fwhere A =

D d = largest acceptable diameter

Ads s f fs s

f A d s

We clearly see that although the interval is symmetric about s0’ in image space, the depth of field interval is not symmetric about s0.

Camera

Large D Small D

More light collected. (slower film, fast action)

Better depth of field.

Better spatial resolution

Human eye

Source: Wikipedia

There are 3 well-known defects in vision due to errors of refraction of the eyes.

◦ Near-sightedness (Myopia): Longer distance from cornea to retina than usual.

◦ Far-sightedness (Hyperopia): Shorter distance from cornea to retina than normal.

◦ Astigmatism: Unequal (asymmetric curvatures) in the corneal surface.

Human eye

Note: The distance for best viewing for adult is 25 cm.

Human eye

GTLE:

Near-sighted person

1 1 1

If s is large, s = f

Since this is a diverging lens, s < 0.

s f s

A near-sighted person has a far point of 100 cm and a near point of 15 cm.(a) What f of the lens should be to move the far

point to infinity?(b)With this correction lens, can this person read a

book at the normal near point (25 cm from the eye)?

Example

The magnifying glass is used for better spatial resolution in image.

On the other words, it helps us to see smaller objects or to be able to distinguish finer features.

Magnifying glass

Magnifying glass

1 1 1

f > 0, s < 0, s , this yields s < 0 (virtual image)

1

s f s

f

s sM

s f

What does “20x lens” mean?

Example

The magnification of small objects is achieved by the use of two postitive lenses: objective lens and an eyepiece.

Microscope

The magnification is approximated by

The standard tube length is 16 cm.

By viewing with the microscope, the image formation may be drawn as

Microscope

0

.e

e

s TM

f f

Example

Example

Telescope