- [Instructor] Welcome.
In this section, we're going to take a high level review
of system parameters.
The goal here is to introduce important parameters
that you should fully understand before going on to more
complex optical design topics.
So the seven parameters we're going to be looking at
are working distance,
field of view, sensor size, resolution, depth of field,
primary magnification,
and F/#.
By the end of this section,
you should have a qualitative understanding
of all of these parameters and some idea
about how some of them will relate to each other.
So jumping right in,
working distance is the distance from the lens
to the object under inspection.
Some systems such as microscopes
are designed to work at a specific working distance.
So your object will always be
the same distance from the lens,
whereas other systems,
such as a traditional photography camera,
are designed to be adjustable
so you can use it at many different working distances.
Field of view describes the area
that is imaged by the optical system.
The field of view is not always the same in every dimension.
In fact, it's usually not.
The vertical field of view and the horizontal field of view
have different magnitudes which are related
by the aspect ratio.
Lens parameters are generally given
in the horizontal field of view.
So if you then want to figure out your
vertical field of view parameters,
that's where the aspect ratio can convert
from one to the other.
angular field of view
is another common way to designate what the field of view is
and it is given by the angle between the rays
coming from opposite sides of the field of view.
So if we were to look at this image here,
this is my field of view,
then rays coming from opposite sides
have some angle labeled theta here between them
which is the angular field of view.
It's common for field of view
to be given as half angular field of view.
So you should make sure you know which is being specified
to avoid a factor two error.
The field of view and the angular field of view
can be related using some trigonometry
with this line drawn directly from the lens
to the field of view.
We form a right triangle.
So the tangent then of the half angular field of view
is equal to the field of view
divided by two times the working distance.
So we can see that as the working distance changes
for a set angular field of view,
the field of view will change in size.
The closer the object gets, the smaller the field of view.
sensor size is the size of the component
that is actively collecting the light that's being focused
by the optical system.
The sensor is often one of the more
expensive components in the camera.
So it is important to optimize what you're doing
with your sensor to get your best quality images.
There are a wide variety of sensor sizes.
They can come from as small as two millimeters
up to as large as 90 millimeters.
We want to make sure you're maximizing
what you can get out of the sensor.
So here's some examples here.
Let's say we have an object and we're imaging it with a lens
and we want to place a sensor in our system.
If a sensor is too small,
then much of the light that is being focused by the lens
is going to miss the sensor entirely
and we're not recording that part of our object.
If our sensor is too large, like on the bottom here,
we're collecting all of the light
that makes it through the optical system,
but a large portion of our sensor is not being used.
This middle case here is the optimal case
where the light collected by the system
makes maximal use of the sensor area.
Next up, resolution is a measurement of an imaging system's
ability to reproduce the details on an object.
The type of resolution you can get
is influenced by a number of factors,
from the lighting used,
to the pixel size on the sensor
and the capabilities of the object.
So depending on the qualities of each of these things,
a different thing may be limiting the resolution
you're able to get in your system.
The easiest to quantify is the resolution
that's limited by the sensor.
So if we look at the number of horizontal or vertical pixels
on a sensor and we divide that into the size of an object,
it will indicate how much space each pixel
covers on the object
and it can be used to estimate resolution.
So for example, if we have a thousand pixels
and we are imaging an object that is one meter tall,
then each pixel covers 0.1 centimeters on the object
and you are never going to get resolution
that is better than that
'cause you can't have multiple pieces of information
on a single pixel.
However, it is a little more complicated than that
because just because information is on two different pixels
doesn't mean that information is distinguishable.
So if we look at this case here,
this is what we call a line pair.
So you have two dark pixels separated by a light area
and in this imaging system here,
the information from each of these dark squares
ends up on adjacent pixels.
However, these are not resolved
because just because the information is on different pixels
doesn't mean we can tell where one starts and one stops.
We need some separation between them.
So over on the right here,
we have an example where there is a larger white gap
between the line pair,
and so the information ends up on separate pixels
with another pixel in between them which is white,
which means this information is resolved.
So line pairs is a common way to specify
your resolution of an optical system,
essentially saying what is the spacing of two dark pixels
that we can resolve?
Now it's a little more complicated
than just saying black and white
because pixels come in gray scale.
So instead of black, white, black,
what we really end up with is dark, less dark, more dark.
So it, depending on what that contrast is,
we can either say they're resolved or not.
Depth of field is a measure of the image quality
produced by stationary lens
for objects at different working distances.
So what range of distances from the lens
will you still be able to produce a quality image?
We should note the depth of field
doesn't really have any meaning except in context
of a specific resolution.
So for example, if we look at these blocks here,
we can see they're getting more and more out of focus
as they get further away from the lens.
But what we consider a sufficiently good focus
depends on the application.
Typically we use these things called performance curves
of a lens to relate the contrast
to the depth of field.
And a 15% to 20% contrast
is the minimum contrast for acceptable image quality.
Again, this is just a bar that's commonly used
and it will depend on your application for what you consider
a sufficient contrast.
So these are some examples of performance curves.
Don't worry too much about the details,
just know that they represent the contrast
that is given by the optical system
for different working distances.
And the depth of field is the range of working distances
where we get at least a 20% contrast.
And here we have a comparison for two performance curves
for identical optical systems,
except that they have different focal lengths
for the lenses.
So we can see that for the shorter focal length,
the 200 millimeter focus,
the depth of field that is achievable
is less than it is for the 500 millimeter focus.
So what depth of field you can get depends on
the optics that are in your system.
The primary magnification of a lens
is defined as the ratio between the sensor size
and the field of view.
So essentially this is telling you
if you map your pixel size onto your object,
how much area on the object will it take up.
So it's very much related to the resolution
that's being limited by pixel size.
In fact, we can say our object space resolution
is the pixel size over the primary magnification
of the system.
F/# pronounced F-number
and written as F backslash pound sign or number sign,
is the ratio of the effective focal length of the lens
to the effective aperture diameter.
Essentially, it's a measure of how much light
is allowed through the system.
So if you have a larger aperture, you have a smaller F/#,
and if you have a smaller aperture
letting less light through,
you have a larger F/#.
And a F/# of three for example,
would be represented with the notation
F/3.
F/# is related to a lot of different parameters.
In particular, your depth of field
will change with your F/#.
So if we consider this image below,
let's say we have a low F/#
which means a large aperture
means light is able to get into your camera
from a wide variety of angles.
And this limits the depth of field that you're able to see.
Whereas if you have a small aperture or a high F/#,
the light's only able to get in a smaller range of angles,
so smaller region of the lens.
This gives you a larger depth of field.
These are sometimes called slow and fast imaging systems
because a large aperture lets a lot of light in.
So a shorter exposure time
gets the same amount of photons into your system,
whereas a smaller aperture lets less light in
and takes a longer exposure time.
Again, we can look at these performance curves
for different lenses that have identical parameters
but different F/#s.
And what we can see is that the contrast
to get a 20% contrast,
there is a smaller range of working distances
for the smaller F/# or larger aperture.
And for the larger F/# or smaller aperture,
the depth of field is larger.
So in summary, we have these seven parameters,
the working distance, field of view, sensor size,
resolution, depth of field, primary magnification, and F/#.
And hopefully you have an idea of what all of these mean
and how some of them are qualitatively
related to each other.
We'll be going in more depth into various parameters
later in the course.
This has been a high level review of system parameters.
Thank you for watching.
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