[Laser] Re: Can anyone explain what a Steradian

[TWOSIG at aol.com]

I think I sent this direct to Paul when I meant to post  it. 
 
 
 
Paul
 
I hope this will help you with the concept of a steradian:
 
Imagine that you are a magician, who among his other powers can take the  
form of an ant.  One day while traveling as an ant you walk into a toy  balloon.  
Then a child picks up the balloon and blows air into it.   The balloon makes 
a small but perfectly round sphere.  Using some  of your magic go to the 
center of the balloon and by magic you stay at its  center.  The child picks up a 
marker and draws a circle, a square, and  a triangle on the skin of the 
balloon.  Once upon a time, I was a  Geometry teacher, and this child was one of my 
students, so naturally the  circle, the square, and the triangle were drawn so 
they have equal areas.  
 
>From the center of the balloon you look out and see these very nice  
geometrical shapes.  You decide to take a picture of the shapes.   ( Of course any 
magician traveling as an ant will have his camera with him!  )  Just as you have 
finished taking the picture, the child starts blowing  more air into the 
balloon, so it gets bigger.  The balloon is still  perfectly round, and your magic 
keeps you in the center.  So you take  another picture.  Then the child blows 
still more air into to the balloon  and it gets even bigger.  It is still 
perfectly round, and your magic still  keeps you at the center of the balloon.  
Yes, you take a third picture of  the circle, square, and triangle.
 
Then the child does what many children do with a balloon, he lets it go  
flying around the room.  This makes you dizzy, so with a little extra magic  you 
help it fly right out the window and land softly in the grass.  You  decide to 
get out of the balloon and go home before that crazy kid comes outside  and 
finds the balloon and blows it up again!
 
Back at home you print out the three pictures that you took from inside the  
balloon.  Then you notice a very strange thing.  In all  three pictures the 
circle, the square, and the triangle are all the  same size.  You know that as 
air was added to the balloon it got  bigger.  It just so happens that as the 
balloon got bigger, the skin  of the balloon got further away from the center 
(where you were when you took  the pictures).  The shapes drawn on the balloon's 
skin grew, but they got  further away.  From where you took the three 
pictures, they looked the  same.
 
Having told this little story, I want to describe this more like a math  
teacher.   The steradian relates to an area on the surface  of a sphere in the 
same way that a radian (or any other measure of angle)  relates to a length on a 
circle.  I used three shapes with the same  area and a balloon that changed 
its size, to stress the idea that a  steradian measures something that relates 
to an area and distance, just in the  same way that degrees, radians, and grids 
measure something that relates to a  length and distance.
 
Small circles, large circles, all have 360 degrees or two pi radians.   The 
length associated with one degree on a small circle is in direct proportion  to 
the length of one degree on a large circle as is the proportion of the  
diameters of the two circles.  The relationship between an area on the  surface of 
a small sphere compared to an area with a different shape on the  surface of a 
large sphere is similar, but my experience tells me it is  a lot harder for 
most people to grasp.
 
When I try to visualize using steradian, I think of two spheres.   The first 
is the celestial sphere, which is a sphere with an infinite ( or at  least 
immense ) radius, and I am standing at its center.  I then try  to mentally 
project a shape on the inside of the sphere -- it could be a  circle, ellipse,  
triangle, square, trapezoid, rectangle, or just a  blob.  I then project the 
shape down onto a small sphere, sometimes a one  foot radius sphere that I am 
holding.  If I measure the area of the shape  on the small sphere, that is the 
number of steradians.
 
For experimenting with light communications, I think of steradians being  
used when you divide the area of a light sensor by the focal length of optical  
system.  ( Using the same units of measure. )    As a  practical matter, I 
don't use it much.  I prefer to think of field of view  in terms of milliradians 
(or degrees) left to right by milliradians (or degrees)  up and down. for a 
rectangular sensor.  If you need to compare different  shapes, steradians might 
be better.
 
Another way steradians are used is for transmitted beams, such as an RF  
antenna, a flashlight, or an LED.  I do not find this very useful, and  perhaps 
someone else should try to explain what the number mean.    However, I think 
that the rating of 5 milliwatts per steradian is the peak at  the center of the 
beam.  If the half power beam width is 40 degrees, then I  think the reading at 
20 degrees from the center of the beam should be 2.5  milliwatts per 
steradian.  
 
If I was going to put a collimating lens in front of the LED, I would  choose 
a lens that had a focal ratio of 1.3 or less.  If the focal ratio is  larger, 
more of the emitted light will be lost because the lens would be  too small 
at the collimating distance.
 
 
Hope this helps.
 
James
N5GUI
 
 
 
 
 
 
In a message dated 3/23/2005 6:45:25 P.M. Central Standard Time,  
Paulc at snet.net writes:

Hello  Folks,

I was wondering if anyone can explain what a steradian is?   I can look up
the formula no problem but conceptually I have a  problem.

For instance

IR diode one has a 1/2 power beamwidth of  40 degrees and has 5 milliwatts
per steradian.

Another diode has a  1/2 power beamwidth of 10 degrees and has 50 or 100
milliwatts per  steradian.

Both draw the same current.

Can the steradian rating  be thought of as a intensity per given area?  Is it
that simple,   so as a higher mW/sr  would be more intense?
So if the power consumed  by each diode is the same, the only way this could
be accomplished is  through beamwidth??

Thanks so  much

PaulC
W1VLF