Petzval Introduction

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En provenance du cours de University of Colorado Boulder

Design of High-Performance Optical Systems

3 notes

University of Colorado Boulder

Design of High-Performance Optical Systems

3 notes

Cours 3 sur 3 dans Specialization Optical Engineering

Optical instruments are how we see the world, from corrective eyewear to medical endoscopes to cell phone cameras to orbiting telescopes. This course extends what you have learned about first-order, paraxial system design and optical resolution and efficiency with the introduction to real lenses and their imperfections. We begin with a description of how different wavelengths propagate through systems, then move on to aberrations that appear with high angle, non-paraxial systems and how to correct for those problems. The course wraps up with a discussion of optical components beyond lenses and an excellent example of a high-performance optical system – the human eye. The mathematical tools required for analysis of high-performance systems are complicated enough that this course will rely more heavily on OpticStudio by Zemax. This will allow students to analyze systems that are too complicated for the simple analysis thus far introduced in this set of courses.

À partir de la leçon

Field Curvature and Distortion

This module continues to discuss monochromatic imperfections in optical systems. We introduce field curvature and distortion so that you may recognize them in your own systems and then summarize the causes and effects of 3rd order aberrations along with the mathematical tools to describe them.

Petzval Introduction4:25

Petzval Wavefront Error0:56

Petzval and Astigmatism3:07

What is Petzval Radius?6:26

Rencontrer les enseignants

Robert McLeod
Professor
Electrical, Computer and Energy Engineering
Amy Sullivan
Research Associate
Electrical, Computer and Energy Engineering

So at the beginning of the last section,

we listed Maxwell's three criteria for perfect imaging.

The first one was ray aberration.

That when you launch rays from a point in the object plane,

they should land ideally at a single point in the image plane.

We saw that spherical aberration,

chromatic aberration and astigmatism tended to break that conditioning,

they tended to to spread the rays out.

It turns out the next set of aberrations

violate Maxwell's second condition and that's that

the rays should fall in a plane in

the image space if they were launched from a plane in the object space.

This is known as field curvature,

and is our next general problem that is caused by the same set of ray aberrations.

So, we're going to look at those now.

The first one is called Petzval,

for a person who first person who looked at this.

It's the fourth term before here.

Like astigmatism, it has this character of rh squared,

still a third-order aberration,

the sum of the powers here is three.

But it's got some different trigonometric functions

and that's just generated from that ray aberration polynomial,

where we took all any possible function,

took the derivative of the x and y ray coordinates with respect to

rh and theta and kept the terms that obey the symmetry conditions.

The difference between Petzval and astigmatism,

and they are actually quite related,

but the difference here is that we see the same behavior,

it looks like a defocus,

that defocus depends on h squared,

and we'll look at that in more detail now,

but the two terms are equal in x and y.

I put a three here before in the case of astigmatism.

That meant the defocus wasn't the same in x and y.

Here it is.

So, what does it mean? What does it do?

Well, let's imagine we started with a point with h equal to zero,

like all aberrations say of spherical,

that means we get perfect imaging if we only had Petzval because if h is equal to zero,

x and y, the ray errors are equal to zero.

Hey, life is good. Now, let's move our object point off some small distance each.

Our image point is going to move off

the axis by whatever the magnification of a system is,

but there's going to be defocus, how much defocus?

Before times h squared.

That's going to be equal to,

I think it was a2, our defocus term here.

So, that would give us for all our rays that we will launch into the pupil,

a linear ray aberration term and that's a defocus,

and it's the same in x and y.

So, we would find once again, a perfect focus,

it's just shifted, it's defocused,

it's not in the perfect image plane.

If we shifted to even larger h,

we'd find quadratically more defocus.

So, we're going to find a focal surface here which

where the rays actually do come to a perfect point,

if this is the only aberration we have,

issues they don't do it at the right place,

they do it on a curved,

quadratically curved in this cubic aberration view of the world,

this third-order aberration, we find a quadratic focal surface here, the Petzval surface.

This is a pain because if I have a piece of film or I have a silicon detector,

they are not universally,

but almost universally flat and I can't bring all of

my light into focus even though it's in focus

somewhere where the focus is depends on the field arc.

So, that's called field curvature in a general sense and you can

see it's related quite closely to astigmatism and we'll come back to that.

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