FAQ: Distortion Q: What is Distortion? And what isis Distortion?
the difference between local distortion and global distortion? !"#
What
What is the difference between local distortion and global distortion?
A: Consider an an
idealized lens, elow: $"#
Consider
idealized
lens,as assketched sketchedbbelow:
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What is Distortion?
$"#Consider an idealized lens, as sketched below:
As a further simplification, consider only the chief ray (the ray through the center of the As a further simplification, consider only the chief ray (the ray through the center of the pupil).
pupil). As a further simplification, consider only the chief ray (the ray through the center of the pupil).
h
h
θf ov
F
θf ov
F
aann ideal
ideal lens, there s distortion,
no distortion, aheight
nd the oon
f athe
point on he isimage is simply: In anIn lens,
there
is isnonoidistortion,
and the
the
height
a point
on
the image
simply:
Inideal
lens,
there
and
ofhof
aeight point
image
istsimply:
hh ) )) h===F FFtan(
Α
ttan(
an(Α Α Distortion
Distortion
Distortion However, in a real lens the image point “h” may differ from this idealized view. For example,
However,
in a reala rlens
point p“h”
may
idealized
view. vFor
However, eal lthe
ens image
the image oint “h” differ
may dfrom
iffer this
from this idealized iew. example,
For consider thisin situation:
consider this situation:
example, consider this situation: i de a l h
r ea l h
A f ov
A f ov
i de a l h
r ea l h
F
F
The height t of the point “ideal h” is F tan (A). The height of the point “real h” is different. The height t of the point “ideal h” is F tan (A). The height of the point “real h” is different. Such a
tlens is spoint
aid to “ideal
have h”
distortion. The Such height
oftothe
is F tan (A). The height of the point “real h” is different. Such a
lens
isasaid
have
distortion.
lens is said to have distortion.
Distortion is defined as:
Distortion is defined as:
(real h - ideal h) / ideal h
(real h - ideal h) / ideal h
©2012 Wells Research, Inc. | 15 A Lewis Street, Lincoln MA 01773 USA | (p) 781.259.8667 | www.wellsresearch.com Page 1 FAQ: Distortion Here are two possible distortion plots:
Distortion is defined as: (real h -­‐ ideal h) / ideal h Here are two possible distortion plots: Here are two possible distortion plots:
corner
corner of f ield
1%
-1%
-1%
1%
center
-1%
1%
-1%
1%
center of field
Both lenses have about 1% distortion, a value that is normally acceptable, even
like cameras.
Both Both lenseslenses have habout
1% distortion,
a value that is normally acceptable, even in visual instruments
ave Local
about 1distortion:
% distortion, a value that is normally acceptable, even in visual like cameras.
instruments like cameras. Besides the absolute value of distortion, it is also important to consider the loca
1 .0 %
0.5 %
0 .5 %
1.0%
curve.
LocalLocal distortion:
distortion: Besides
the absolute
value vof
distortion,
it is also
to consider
the local
the distortion
Besides the absolute alue of distortion, it is important
also important to consider the slope
local of
slope of Consider
the
two
curves
above.
The
lens
on
the
right
has
a problem
at the edge
curve.the distortion curve. Consider the two curves above. The lens on the right has a problem at numerical example may clarify the problem:
the edge of the field. Consider
the two curves above. The lens on the right has a problem at the edge of the field. A
numerical
exampleexample may clarify
problem:
A numerical may the
cpoints
larify the Consider
A and B:
problem: 10.0 m m
Without d
istortion t
he h
eight o
f p
oints Consider points A and B:
A
9.9 m m
A and B would be 10 mm and 9.9 mm 10.0 m m
B
respectively. A
9.9 m m
B
With distortion, the heights are hA = 10 mm x ( 1 – 1.0% ) = 9.9 mm hB = 9.9 mm x ( 1 -­‐ 0.5 %) = 9.85 mm Two points that should appear 1/10 mm apart will appear to be separated by only half that distance. -1%
-1%
1%
1%
Without distortion the height of points A and B would be 10 mm and 9.9 mm r
Without distortion the height of points A and B would be 10 mm and 9.9 mm respectively.
©2012 Wells Research, IWith
nc. | 15 A
Lewis Street, Lincoln MA 01773 Uare
SA | (p) 781.259.8667 | www.wellsresearch.com distortion,
the heights
With distortion, the heights are
Page 2 FAQ: Distortion A real world example: The author found out about this problem the hard way several years ago. The product was a scanning display, and the output from the prototype looked like this: What was expected: What appeared: The problem was a distortion curve exactly like the one presented above. Total distortion was fine. Local distortion was severe. ©2012 Wells Research, Inc. | 15 A Lewis Street, Lincoln MA 01773 USA | (p) 781.259.8667 | www.wellsresearch.com Page 3