[Laser] Re: Fresnel lenses

[TWOSIG at aol.com]

Paul
 
As a former Geometry teacher, I wanted to put in a comment ( or 2 pi  )
 
The formula that you have for field of view is a simplified formula for the  
length of an arc.  In this case you divide the length of the arc by its  
distance from you, so that you end up with only angles as your units.  The  value 
57.3 is a close approximation for the conversion from Radians to Degrees,  
there being 360 degrees in a full circle, and also 2 pi Radians.  ( Purists  would 
probably say that Radians are not units like Degrees, having been formed  by 
dividing the length of an arc by the length of a radius, thus you have a  
dimensionless pure number. )
 
I prefer to visualize field of view as two similar triangles with the  "lens" 
(or a point in the middle of it) as the common apex.  If my lens has  a focal 
length of 300 mm and my detector (or film in the case of a camera) is 10  mm 
wide, then I draw a line from the left side of my detector through the center  
of the lens.  Then I draw another line from the right side of my detector  
through the center of the lens.  The field of view of the "lens - detector"  is 
then bounded by those two lines.  At 30 feet from the lens, the field of  view 
spans 1 foot.  At 300 feet from the lens, the field of view spans 10  feet.  
At one mile, 176 feet.  And so on.
 
To convert that to degrees, the first thing we do is pretend that the  
detector, or the space we are looking at, is curved like an arc with a radius  equal 
to the distance we are using.  (Rather than try to do the  trigonometry, 
which would be meaninglessly precise, we make everything parts of  a circle.)  
Then we divide the width of the detector by the product of  the focal length 
times 2 pi.   At this point we have calculated the  fraction of a full circle that 
is our field of  view.         The last step is to put it  into the desired 
units.  If you are working with degrees, you  would multiply that fraction of a 
circle by 360 degree.  If on the  other hand you were working in radians, you 
would multiply by 2  pi.    The interesting thing is that if you knew ahead 
of time  that you were going to be using radians, you could go back to the 
previous step  and NOT divide by 2 pi and then NOT multiply by 2 pi in the last ste
p.
 
In essence, the formula simplifies to the width of the detector divided by  
the focal length.
 
If it helps, just sketch a circle with the lens at the center and the  
detector as part of the arc.  Then  the field of view of the  detector is the 
fraction of its width to the circumference of the circle.
 
 
 
Best wishes.
 
James
N5GUI
 
 
 
In a message dated 6/13/2005 4:42:12 P.M. Central Standard Time,  
paulc at snet.net writes:

Hey  Tim,

Thanks a bunch for the time to answer my email.
I was never  sure if the answer came out in mR or in degrees.

Where does the  constant 57.3 come from?  I have seen formulas  that state 
FOV =  detector dia/ focal length.

I have a 1 watt laser diode that I want to  collimate a single 5" lens.  The 
diode has a fiber output angle that  closely matches a 5" lens I have.

I have been doing some experiments  with an 808nm at 150 mw if you want to 
see a pix of cloud bounce at straight  up I have that I can send you. Also Have 
a clear sky night trace of signal  return as well.

Both are graphs showing noise floor and the 1 Khz  square wave.  Boy does the 
signal pic up when you follow the light column  up and finally hit the dot on 
the clouds.

hi pau\
i'm using a short  focal length mirror for some NLOS
experiments and it has a FOV of about 0.7  degrees or
so. (247mm focal length and 3x3mm detector)

here's a  formula for calculating field of view:

F = (57.3/FL) x  D

where:
F= field size in degrees
FL = focal length of lens or  mirror in millimeters
D = detector or film dimension in  millimeters

for your example:
57.3 / 400mm = 0.14325
0.14325 x  2.5mm = 0.358 degrees FOV

in milliradians:
milliradians = degrees x  17.45
0.358 x 17.45 = 6.247 mR FOV


>
>From: "Paul  Cianciolo" 

>Subject: [Laser] Fresnel  lenses
>
>Folks,
>
>I wonder if anyone has used a 10"  or so diameter for
>a receive antenna?
>
>The problem I see  is the relatively short focal
>lengths. This combined with the a 2.5 mm  dia.
>detector makes for a pretty wide FOV.
>The fresnel's have  tried have not been the most well
>focused lens's.
>Just  curios.
>3DLEN.COM perhaps?
>What are you guys using as a FOV for  NLOS receivers?
>W1VLF
>PauLC
>



Tim  Toast
http://www.aladal.net/toast/exp.html



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