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WP's Lens Calculator


Format filling imaging

Focal distance calculator

Easy to use calculator for the distance to object with given focal length and for focal length with given distance to object keeping the condition of format filling imaging. Thus making best utilization of the photoactive area of the imaging medium. (JavaScript required.)
Please type in a full stop . as decimal punctuation mark and take notice of the different measurement units.
(By the way: 1 inch = 25.4 mm, 1 foot = 304.8 mm, 1 yard = 914.4 mm = 0.9144 m, 1 mile = 1 609.34 m)



Lens optics
Refraction with thin lenses

Focal length

d = f (1 + O / S)

f = d / (1 + O / S)

Focal length f [mm]:

Distance d [m]:

Object size O [m]:

Object size O [m]:

Image size S [mm]:

Image size S [mm]:









Caution: One has to keep at least a distance of 0.3 m (sometimes more than 1 m) using standard lenses, otherwise they cannot provide sharp images.

By the way the real sensor size can be estimated when transforming the equations given above. Object size O and object distance d are just measured in a test set, the focal length f is that of the lens inscription: S = f O / (d - f); [all values in mm].


Depth of field (or depth of focus)

Each of the following terms, i.e. their sum, give the depth of field (or depth of focus) region where objects are in focus, thus appear sharp. (All in SI units - meters or millimeters.)
The in-focus region in front of the set distance is:

dfront = d f / (f + k (d - f))

And the in-focus region behind this distance is:

drear = d f / (f - k (d + f))

Signs and symbols:

The diameter of the circle of confusion is given by the minimal distance of two spots the human eye is able to identify from a certain distance. A standard value is 2 angle minutes from 250 mm distance, thus 0.0145 mm. Or 6 line pairs per millimeter as well. (Strictly speaking one has to calculate this from the output medium to the sensor or film, resp. backwards ;-) A rule of thumb is: = diagonal of the sensor [in mm] / 1 000 ... 1 500.

Setting d to so-called hyperfocal distance h = f (f / (k ) + 1) makes the region starting at h/2 to infinity appear in focus. Many simple cameras work in this way.


Equations of movement

Estimating the size of the interesting area of moving objects and the occurring velocities, here the equations of movement in simple form. (All in SI units meters and seconds.)


Straight movement

Signs and symbols:

v = v0 + a t

w = v0 t + a/2 t

2 a w = v - v0


Orbit movement

Signs and symbols:

Orbital velocity: v = r ω


Free fall and inclined plane
Free fall and inclined plane

Free fall and inclined plane

Basic principle is the conservation of energy: Epot = Ekin. Hereby the mass of the object is abridged. Friction is supposed to be negligible. And - important - the object must not significantly gather rotation energy, thus it should preferentially glide down the ramp without much friction. (But for a car - model or real - the formula works.)

Signs and symbols:

v = √(2 g h)
h = 1/2 v / g


Special cases

Every theory finds its challenge in reality...

Motion blur

During exposure the object moves the distance

Δw = v tshutter

the product of its velocity and time of exposure of each frame.

Example: A car moves with constant velocity v = 64 km/h = 17.78 m/s. With a frame rate F = 1 000 frames/sec the car will change its position in one frame up to

Δw = v t = v / F = 17.78 m/s / 1 000 frames/sec = 0.01778 m = 17.78 mm

if one does not reduce the time of exposure for each frame by using a shutter. If the image of Δw is smaller than one pixel, the effect will not be visible.


w = 2  d  tan ω
Stretching resolution by cross movement

Cross movement - diagonal view at the object

If the camera does not perpendicularly look onto the object, but an angle different from 90 lies between camera view and object or its direction of movement, resp., e.g. if a vehicle moves towards the camera, thus the distance to be caught is reduced to about

w|_ = w' sin α

with w|_ as perpendicular component of the drive path w' and the angle α between viewing direction and vehicle drive path w'.

As the figure on the right shows one is possibly able to gain some more path when selecting an appropriate setup.
So one has the chance to capture more details in space and time, thus imaging the object and its movement in higher resolution.

In this setup, however, one must take in consideration depth of field, because the distance to the camera may heavily change.




WP (1998 -) 2012
Update: V8.4, 2012-03-02