Optical instruments are how we see the world, from corrective eyewear to medical endoscopes to cell phone cameras to orbiting telescopes. When you finish this course, you will be able to design, to first order, such optical systems with simple mathematical and graphical techniques. This first order design will allow you to develop the foundation needed to begin all optical design as well as the intuition needed to quickly address the feasibility of complicated designs during brainstorming meetings. You will learn how to enter these designs into an industry-standard design tool, OpticStudio by Zemax, to analyze and improve performance with powerful automatic optimization methods.
The Lens Catalog
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来自 University of Colorado Boulder 的课程
First Order Optical System Design
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从本节课中
Optical system design in OpticStudio
In this module, you will learn how to enter the description of an optical system into OpticStudio, analyze the performance of that system using various calculations and plots, and finally optimize that design by defining a merit function and search variables.
与讲师见面
Amy SullivanResearch Associate
Electrical, Computer and Energy Engineering
Robert McLeodProfessor
Electrical, Computer and Energy Engineering
Now, let's take a second tour through
OpticStudio and use it in a slightly more sophisticated way.
In our previous example,
we entered lens curvatures,
thickness and glasses in order to design a lens.
A relatively common second way to use the program is to want to design
an optical system using catalog or stock parts that one could order from vendors.
At first, like most CAD programs,
OpticStudio contains a libraries of the materials and the parts that one can buy,
so that you can simply pull those into your designs.
You don't have to go into them one-by-one.
So, the first thing we're going to do is look at the libraries tab.
Now, before I mentioned N-BK7,
a common glass, let's go find that.
So I clicked on the materials catalog.
This is all of the standard materials which the program knows about.
The catalog here is basically the vendors, or the vendor catalogs of glasses.
These are glass manufacturers.
Hoya, for example, is a relatively a large glass manufacturer.
Under misc you find things like wire and other miscellaneous things.
Let's go down to the Schott catalog right here.
And now, in the Schott catalog,
this is all the glasses that they make.
These are their part numbers.
And if I go down a little bit here,
I will get to N-BK7 ordinary glass.
And you see other BK glasses.
There's N-BK10.
N-BK7, now I can look at.
It has an index,
that's the N at the sodium D-Line.
We'll come back to that momentarily but it just specifies a color,
it's yellow of 1.51, and decimal points.
So now, I know the index of the glass.
This V number here is an important thing
that tells us how much the index changes with color.
But it also knows things like the coefficient of thermal expansion.
And so, we can do designs where we use temperature
to understand how they vary over temperature etc.
The point is there's a lot of sophistication built into this.
It knows a lot about the materials.
So we don't want to use that this time,
but the point is is you can go select glasses with all sorts
of properties and there is even search metrics
and tools to help you analyze and find the right glass.
What we're interested in this time is the lens catalog.
We don't want to build our own lens,
we want some other optical design to do that for us.
So, I'm going to call the lens catalog.
Once again, we have the vendor catalogs here.
Let's see, here is Nippon Sheet Glass.
These are green lenses.
Here is Sigma etc.
I'm going to call Thorlabs and click those for a minute and downside
here is every Thorlabs lens in the catalog or the program knows about.
The first thing is the part number,
and the second thing is the focal length,
and then finally the diameter of the lens.
This is way too many parts for me to worry about,
so over here, we have some search criteria that'll help us find the lens we want.
I want about a 50 millimeter lens,
so I've entered about 48 to about 52 millimeters as the focal length of the lens.
And if you don't know what that word means, that's okay.
And I want lens that's about an inch or 25 millimeters in diameter.
So I've entered a search range there.
And I also want a doublet,
a lens that's made of two pieces of glass,
instead of say a singlet or a triplet or four,
five and six elements.
Now, I've got into a much more reasonable set-up lenses that I can look at.
And let's just look at one of those.
So I'll just pick the first one and say show me its layout.
Now if you notice, this looks a lot like that cross-section
we saw with the camera sawed in half.
We saw lenses that looked a lot like this.
This is two glasses with some positive and negative curvatures.
So I like the looks of that one,
I'm going to insert it into my design.
So I'll click insert.
I have to decide where to insert it.
Remember our design,
our lens data editor is a table of services starting from the object,
sequentially hitting every object and ending at the image.
So I'll insert this lens at one, seems okay.
I'll say okay.
And close this.
So now, I have an object and now have this lens.
The comment here gives me the part number of the lens, that's kind of nice.
I see some curvatures, some thicknesses.
So new glasses, Here's SF10,
another pretty common glass.
And that front and back services have anti-reflection coatings on them.
And finally, somebody who orders the lens,
notice this is half an inch, so just what I wanted.
Now, in my layout,
I still don't see the lens.
This is the mistake you always make because we
haven't launched any light into this lens yet.
So we're not going to see anything going on here until
the program knows about some light being watched into the system.
So to do that,
let's first move the Stop.
When we inserted this lens,
the Stop, you always have a Stop in the system.
That's the thing that controls where the light goes.
The Stop is now down here,
off the end of the lens, and I don't want that.
I'd like the first surface of the lens to be my Stop.
So, I'm going to click on the first surface.
And if you notice up here, there's a little pull down menu, Surface Properties.
I'm going to click on that.
And now there's all sorts of things I can do to that surface.
For example, it's aperture.
Right now, the aperture is surf standard but I can do things to it.
I can make it square and all sorts of fun things.
I can tilt or de-center the surface.
If you remember that mirror that was in the viewfinder system of the camera,
this is how you tilt.
We tilt that mirror in order to change the optic axis.
The coating is specified here, so, it's all good stuff.
But what I want to do right now is simply make this surface the Stop.
And when I do that, I now see that the Stop has moved up to surface one.
All right, that's good but I still haven't told
the system how I want to launch light at that Stop.
Let's go back to our System Explorer over here.
If it doesn't show, I go to set up and click System Explorer and it
brings it up, and my aperture.
So, before we use float By Stop Size,
let's just do again.
And now we see our lens.
So, I just opened and closed the window,
so I wasn't sure why it was, it needed to be reset.
So, my object is that infinitely far away,
and let's do a finite distance now.
Maybe a 100 millimeters.
As is always the case, this lens,
this diagram here didn't know it should include that first surface.
So at the moment it's showing us rays from surface one,
and it shows us the comment there, what part that is.
I'm going to start from surface zero.
Couldn't have done that before because surface zero is infinitely far away.
Oh that's nice.
Now, I have a single field point.
It's launching a cone of rays and those cone of rays fully fill the surface.
And that fully fills that first surface because that surface is the Stop.
And I told the system that the aperture I wanted was to fill up the Stop.
It turns out that it's actually not the best idea.
Lenses are ground,
and the grinding process is less accurate as you go right off to the edges.
And so, it's typical that lens manufacturers specify a clear aperture or clear diameter.
This is the part of the lens you should use as a part,
as opposed to how mechanically large it actually is.
This is a one inch diameter lens that you shouldn't actually try to use that whole inch.
So, I'd like to bring the cone of rays down, and I don't want to do that
by reducing the semi-diameter of this lens because that's how big this lens is.
So instead, I'm going to go back to my aperture type over here,
and I'm going to look at some of these options.
One down here is object-space numerical aperture abbreviated NA here.
What NA is the refractive index,
in this case for in vacuum,
so that's one times the sine of the largest ray angle that gets into the lens.
So it's the sine of this angle right here.
And note by the way, N sine theta sounds like a familiar quantity.
That's Snell's law.
That's a really important quantity.
It's actually a conserved quantity, it's an important thing.
That's why numerical aperture is a good variable,
a good thing to know about.
So we're going to choose objects-based NA.
And I guess I don't know what I want
the sign of the angle of the largest ray angle to be here.
So, I'll just pick something, 0.2.
To explore, break this, see what happens.
Okay, so now the cone of rays launched up here is controlled by its angle,
no longer by the size of the Stop.
And if I think about it, 0.2 times 100 would tell me roughly what this point is.
And I see from the coordinates on the diagram,
it's around 20 millimeters.
This is a 12.5 millimeter semi-diameter lens, so that's too big.
Now, there's not really a problem with watching rays that are too big.
These rays are simply chopped off.
They don't make it through the system.
But if my goal was to use less of the aperture of the lens,
apparently I have chosen the value that's too big.
Well, it looks like about half that would be better.
Well, that's nice.
So now, I have 100 times 0.1 my aperture value,
my numerical aperture and that's about 10 millimeters.
And again, you can see that's exactly what the coordinates on the diagram tell me.
Since the semi-diameter of my lens is 12 millimeters or 12.5,
10 is about right to fill but not overfill the lens.
So now I've controlled my cone of rays.
I control the aperture in a more sophisticated way.
The next thing I'd like to do is put some more field points.
This is a rather boring object it's a single pinhole,
it's a single spherical wave.
I'd like to look at some other field points.
So, let me open the field dialog here.
Now, currently I see that the field type,
how I'm telling the program what the field points are using an angle.
An angle is the thing to do when the object is infinitely far away.
It's very awkward to say the height of
an infinitely far away object is some fraction of that infinity.
But now my object's 100 millimeters away,
so I'm going to choose object length.
Now, I specify field points by their distance off of the axis here.
Of course, the sky was zero so it didn't change, it didn't matter.
I see one field point X equals zero, Y equal zero.
Y is by default this coordinate and Z down the axis.
So, I'm going to choose,
I'm going to add some points and I want to give them some different Y values.
So, I will add a field point and need to enable it.
You can enable and disable field points,
so you can turn them on and off.
And I don't know, five millimeters.
That's exciting.
So now, my diagram updates and I see two field points.
The second one that you can check,
it's a five millimeters, is colored green only to make the rays easier to see.
That doesn't mean it's green light.
You can choose how you want to color things.
This is only for you.
Note that these two points launch cones of rays,
both for the cones of rays have an NA of 0.1 numerical
aperture and both of them intersect in the stop.
That's what it means to be the stop.
This is why the stop position is very important.
If I had chosen the stop to be some other surface in the lens,
then these cones of rays would intersect perfectly at that surface.
The stop is very important for controlling where the light is going,
what light you're launching off the object.
Well, that was fun. Let's do it again.
Let's add another field point there, enable.
Notice there's this little table here, if you'd like to work on a table instead
and the weight 10 millimeters,
five is good, 10 is better.
Let's close that.
And again, we see now another field point again colored
differently just so you can see them and in the settings,
you can change how you color things.
And again, all three cones intersect at
the stop and you can see now that this most extreme field point,
the light with a 0.1 numerical aperture is tilted downward.
And that matters in terms of how the lens works.
If I move this stop somewhere else I might change
the tilt of this cone and that would strongly change the performance of the lens.
Okay, now, there are some field points.
Finally, let's open the wavelengths dialog again and
do something a little more interesting with that.
Right at the moment, since we have one wavelength at
0.55 microns, that's in the green.
Maybe we'd like to look at a lens that operates over the entire visible range.
Well, it turns out the program can simulate multiple wavelengths at once.
A very common choice for operating in the visible range is what's
called the Fraunhofer absorption lines.
So again in Fraunhofer you can look in Wikipedia
was one of the first people to point a spectrograph,
a prism basically at the sun and let us through
the dark absorption lines due to molecular absorption of the light.
He very creatively labeled these A, B,C, D etc,
and those are now signposts we use in the spectrum.
Just convenient labels.
So one of the common ways to analyze lenses,
the common set of the wavelengths to use are the sodium
which are the Fraunhofer F, D and C lines,
but little D is the sodium absorption line here.
Fraunhofer didn't know that he was just labeling the number.
So I'm just going to select that preset.
And now I see I have three wavelengths.
Notice this looks a lot like the field or just adding things we want the program to do.
And those are at 0.4, 8.5, 8.65 that's blue, yellow and red.
So now, we have a reasonable view of the visible spectrum.
And that number two this 0.588 microns.
That's that sodium D line,
which is a common place to specify index of glasses.
Now, we can't really see that on this diagram,
if we wanted to playing up the settings here.
The diagram is currently just showing us wavelength one.
I could go ahead and show all of the wavelengths.
Notice, I'm still coloring the rays by the field.
I could color them by the wavelength if I want to and I say okay.
And actually I don't see anything because all of the colors are being launched
exactly the same from the same positions into the same columns.
They all overlap. So it doesn't actually show me much but it's
there and I could see color behavior if I wanted to.
Well, I'm almost done with this system.
I have an object it has some colors, it has some fields.
I've an interesting doublet lens.
What I haven't finished doing is getting on to the image.
So let's finish.
I have a blank surface here and there's no problem with that.
It doesn't do anything but just for fun. Let's go and delete that.
Double click, delete surface.
And now, I see my image, object lens image.
And the last thickness of the lens has a thickness of zero.
So that's the reason I don't see any rays
after the lens is there's no distance in my system.
Let's go ahead and use the same trick we did before.
I'll use A select, click the middle button here and I'll use
a marginal ray height solve zero.
And that gets me pretty close to the image plane.
Now, I have something starting to look like a realistic lens system.
Note that I made some choices here that made this system sort of symmetrical.
If you remember, this is a 50 millimeter focal length lens.
And we're going to see that the one-to-one imaging condition is twice the focal length.
In this case, a 100 in front of the lens where exactly in
front of by the way is slightly sophisticated but
roughly 100 millimeters is twice the focal length
in front of lens and we have roughly 100 millimeters behind the lens.
And so that means this field point here that's at
10 millimeters images over here to about minus 10.
So that's about a magnification of minus one formerly.
So, we can zoom in on that. This is always fun.
And as we've stated before, lenses aren't perfect.
And so you see that the on axis focal point doesn't look too bad,
but as we go off axis they look pretty crazy.
You can see that the plane where they can come into best focus,
well, isn't a plane as a matter of fact,
it's actually a sphere.
That's something called field curvature.
These are the sorts of things we'll worry about later in the course.
So to summarize, we've built a lens,
we pulled one out of a catalog that we could buy.
We've launched multiple field points with
multiple colors and we've traced all the way to the image.
That's a fairly typical set up from beginning to do
a system design as opposed to a lens design.
