In general a lens system can be seen here (first
picture). The Ophthalmic
hyperguide
on Clinic Optics use the nodal points, which are the
same as 'Principal Points' in the
first figure of the earlier mentioned URL: so
the
nodal point is the 'beginning' from where the focal distance
is measured from.
And a general definition of focal length is (coming
for
this link): You actually measure the distance
from the focus to something called the rear (or secondary) nodal
point
of the lens. The strict definition is: Assuming that the lens is
surrounded
by air or vacuum (refractive index 1.0), the focal length is the
distance from the secondary principal point (which in this case is
also
the secondary nodal point) to the rear focal point of a lens.
The Indiana Reduced Eye, General Chromatic Eye and Gullstrand’s
Schematic Eye eye model can be seen in this link.
Reading all the above; the focal length of the eye is
16.67 [mm] (and this is the focal length as seen in the air), which
gives a comparable image size as the eye's lens system with a focal
length of 22.22 [mm] (16.67*1.333); with one side in watery
medium.
The eye's
aperture ranges between 2 mm (in very bright conditions) and 8
mm
(in dark conditions). Together with the focal length (22.22 mm), the
F-number is 22.22/2=11 to 22.22/8=2.8
Visual acuity
The ability to determine and
recognize an object (like a boat, a specific letter or that a
pixel is
experienced as a dot, etc.). This is
around 5 arc minutes for the contour of the object..
Point acuity
The ability to recognize two dots. This is around 1 arc
minute between the dots (inter pixel gap).
Natural stereo acuity
The ability to experience a difference in stereo depth in a
natural
environment is around 10"
Vernier acuity
The ability to experience a difference of two collinear lines is
around 10"
Stereo acuity
The ability to experience a difference in stereo depth in
laboratory
environment is around 2" (Ferwerda [1990],
page 220)
Fovea information
Diameter
of the fovea: 1.5 mm (~5.2 deg); foveola (rod-free,
capillary-free fovea): 0.3 mm (~1 deg)
Pixel pitch and inter pixel gap of displays
Mostly people are interested in the size [cm] and resolution
[pixels/cm] (or pixel pitch [μm]) of a display, and that is of
course
important, but the inter pixel gap [μm] is also important certainly
if
we want to see a display close by (like in a viewer). If the inter
pixel gap is large, it gives these black line artifacts in an image.
It is interesting of course that a pixel is made up of three dots; a
dot for red, blue and green. See for instance this
example.
Several displays has been investigated with regard to the pixel
pitch
[μm] and
inter pixel gap [μm]. These two aspects determine if one can discern
the pixel
size and/or the inter pixel gap. Some findings:
Depending on the viewing distance the inter pixel gap becomes
visible
as soon as it it represent a viewing angle larger than the point acuity. In the below
graph
this relations has been presented:
For example: a viewing distance of 10 cm (like for a stereo viewer:
the
Cyclopital3D)
needs a inter pixel gap of less than 30 μm to be invisible (blue
curve).
To determine that a pixel is large enough to appreciate it as a
square,
the visual acuity comes into play (at 5'). So
that
means that between 1 (point acuity) or 5 (visual acuity) arc minutes
pixelation starts to be experienced. Lets assume that an 2.5' angle
is
enough to cause pixelation (pink curve), this means that at 10 cm an
pixel pitch of
~75 μm would start to be perceived as pixelation.
So it would be nice to have a (stereo)viewer at 10 cm viewing
distance,
which has a pixel pitch < 75 μm (~340 [pixels/inch]), a display
size
of (2x)1280 pixels (to get a viewing angle of 50 deg) and an inter
pixel gap < 30 μm.
The iPod Touch (4th gen) comes close (as it only has a
width
of 960 pixels).
<by the way: a good LCD [like Dell E4300] has equivalent specs, but than for a viewing
disctance of
30-50 cm>
Acknowledgements
I would like to thank the following people for their help and
constructive
feedback: Peter Davis, Ken Burgess, Krishnan and all other
unmentioned
people. Any
remaining
errors
in methodology or results are my responsibility of course!!! If you
want
to provide constructive feedback, let me
know.
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