Lens Parameters
(Part 1 of 2)
Focal Length The focal point of a lens
is the point where the collimated beam, which has all rays parallel,
gets focused to a point. Consequently, the focal point is the image
of an infinitely remote light source. The focal length f is a
distance from the lens to the focal point given in millimeters
(mm).
A thin lens model shows the basic lens
principal. When an object is moved closer to the lens, the image
will be in focus at a distance which is greater than the focal
length.
The following simple lens formula
applies:
where do is the distance
from the object to the lens (working distance), di
is the distance from the lens to the camera sensor and m is
magnification. If we know a magnification and a working distance we
can calculate the required focal length using the following equation:
Typically lenses are far more complex and
consist of a number of lens elements with different thicknesses and
curvatures, designed so that the combination corrects the imaging
defects (aberrations). The focal length of a thick lens is measured
from two planes called the principal planes.
The thick lens acts as though it were a thin
lens placed at the entrance of the lens when considered from the
object side, and at the exit of the lens when considered from the
image side. The principal planes serve as the reference for the
location of the front focal point, back focal point, object and
image positions. The lens equation, for the above simple example,
operates as though the space between the planes does not exist. In
reality, the planes can be crossed inside of the lens or lay
entirely outside the physical boundaries of the lens. Alternatively,
often a back focal length (BF) of a lens is specified, which
is the distance from the rear element of the lens to the back focal
point, and a front focal length (FF) as a distance between
the front lens element and the front focal point.
Lenses are available with a fixed focal
length or variable focal length e.g. varifocal lenses or
zoom
lenses.
Lenses with a focal length of more then
25 mm are telephoto lenses. They make the object appear larger
resulting in smaller fields of view. Lenses with a focal length
shorter then 15 mm are wide-angle lenses. They make the object
appear smaller resulting in larger field of view.
Lens Power (Diopter) The
power of a lens (f
given in meters)
is basically the reciprocal of its focal length:
Lens Aperture (f/Number)
In addition to the ability
to focus light, lenses have the ability to control the amount of light
that reaches the camera sensor. The f/number printed on the lens (fn₯)
is the ratio of the focal length (f) of the lens to the
diameter of the aperture (A) and it is only valid if an
object is infinitely far.
For machine vision applications, the
object is relatively close, hence there are two f/numbers one for
the
object side, and one for the image side.
For close objects fimage is
greater then
fobject
so the f/number will be higher than one shown on the lens. For
example, a lens set at f/4 will act like an f/8 lens at a magnification
of 1.
The f/number of a lens determines
the brightness of the image, depth of field, and resolution of the
lens. Standard f-stops are for f/numbers of 1.2, 1.4, 2, 2.8, 4,
5.6, 8, 11, 16, etc. Each f-stop changes the amount of light
available to the camera by a factor of 2. The automatic aperture
control available for some lenses should not be used in machine vision applications. The automatic aperture control may
compensate for light changes that need to be detected.
Angle of View
Is the angle
subtended by object producing the maximum image size. The maximum
field angle (Qmax)
is obtained when camera is focused to infinity. For machine
vision applications, the object is close and the field angle
(Q)
is calculated using the working f/number.
Field of View (FOV) Is the object
area that is focused by the lens onto the image sensor. Typically,
the FOV should be slightly larger than an area containing all
desired features.
The FOV can be adjusted by adjusting the
cameras distance from the object (working distance) thehe
greater the distance, the larger the FOV. It can also be adjusted by
changing the focal length of the lens the longer the lens focal
length, the smaller the FOV. The FOV can be calculated using
following equations:
The FOV size depends on the size of the smallest detail needed
to be detected. This is also connected with camera resolution.
Good sampling practice suggest a minimum of two samples (pixels)
for reliable detection. Hence, 512 x 512 pixels camera needed
to detect 0.25 x 0.25 mm detail could have maximum FOV of 64 x
64 mm.
Magnification The magnification is:
where V x H is the size of the
FOV, and v x h is the size of the camera sensor. As magnification is
inversely proportional to working distance (do),
care must be taken in gauging applications not to allow any lens
vibrations unless one uses a special telecentric lens.
Depth-of-Field Depth-of-field is the
range of lens-to-object distances over which the image will be in
acceptable focus. The depth-of-field increases with higher
object-side f/number. The object-side f/number (fobject)
is given by:
Also, lenses with shorter focal length
provide greater depth-of-field. Closing the aperture will require
more illumination and using shorter focal length lenses will require
positioning an object closer to the camera. However, moving an object
closer reduces the depth-of-field hence, requiring a compromise.
For more information, please contact
High-Tech Digital Technical Support.
310-265-8203
support@high-techdigital.com.
|
