[Laser] Lenses added to Ramsey receiver

[James Whitfield]

In a recent post, Clint, KA7OEI, pointed out:

"...The Ramsey manual only mentions the use of lenses in passing but should have gone farther in extolling their virtues - that is, essentially noise-free signal "amplification!"  Unfortunately, the packaging of typical phototransistors makes their efficient use with lenses rather difficult - although even very poor coupling of a fairly small (magnifying-glass sized) lens into the phototransistor provides a radical improvement..."

In this post I want to comment and "put some numbers" on that amplification.  For my examples I will use the Ramsey receiver built per the instructions.  This uses the phototransistor, but I hope it is clear that my points apply to any photodetector, so long as its physical characteristics and any inherent optics are considered.

First of all the marketing material claims that the range of the Ramsey transmitter and receiver system is 1/4 mile.  I have not verified that, but will assume it is true for the numbers I present.

The Phototransistor looks like a clear plastic LED, 5mm in diameter.  I have not tried to map the sensitivity of the device versus the angle off axis, which would be the equivalent to the beam angle of an LED and its relative brightness.  This I will also disregard for the numbers.  Please note that if the sensor had been a "flat" plate, I would have presumed that its sensitivity from an off axis direction would have been proportional to the cosine of the angle from the axis.  Also I would have defined the axis of a flat plate as perpendicular to the flat.

Now let us suppose that we have a 50 mm diameter lens.  The aperture of the lens is then 100 times the area of the phototransistor.  The rule of thumb then is that adjusted "properly", one would intersect 100 times as much light as the bare phototransistor.  It is a reasonable assumption as long as the "beam width" of the sensor is wider than the lens.  As a case in point, if the lens was an f/1, meaning 50X50 mm lens, the beam width would need to be uniform over a cone with a half angle of almost 27 degrees.  My own experiments have included 50X300 mm lenses.  The cone's half angle then less that five degrees, so it is far more reasonable to assume uniformity.

So I have set up a 5mm phototransistor with a 50X300 mm lens.  What then is "properly" setup.  Let's run some numbers.

Start with the sensor 250 mm from the lens focal point.  That would be only 50 mm behind the lens ( or the alternate solution of 550 mm behind it ).  The cone of light coming from the target would be less than the diameter of the lens, by a simple factor of 250 / 300 = 0.8333.  That would make its area down to 0.6944.  Assuming no light loss in the lens, the light on the sensor is 1.44 time brighter.

As it turns out the beam from the transmitter expands proportionally to the distance, which in turn means the beam intensity drops off to the inverse square.  The 0.25 mile range jumps to a hearty 0.30.

Move the sensor to 150 mm from the focal point.  The numbers go to 150 / 300 = 0.5  The area is now 0.25 making the brightness 4.0 times.  Range goes to 0.5 mile.

100 mm from focal point - 0.3333   area 0.1111  brightness 9X   range 0.75 mile

50 mm from focal point  - 0.1667   area  0.0278  brightness 36X  range 1.50 miles

In these situations, note that the placement of the sensor "in the beam" has gotten steadily more critical.  Said another way, the direction that the lens and sensor assembly must be pointed becomes increasingly more difficult.  Not much gain, lots of slop in the directionality.  More gain, less slop.

Now consider the case where the sensor is 30 mm from the focal point.  The diameter of the cone is now equal to the diameter of the phototransistor and you have no slop in your alignment.  If your equipment is not perfectly aligned, you will loose some of the light and your system will not perform to the "numbers".  It will still work, and it may even out perform the previous examples, but the "numbers" start to tell you things that you may not be able to actually get from the equipment.

Best case, 0.100 area 0.010 brightness 100X  range 2.5 miles

Double the lens to a 100X600 mm lens.  Adjust the distances for the longer focal length.  Then the best case is 0.05  area 0.0025  brightness 400    range 5.0 miles

Use a 6 inch telescope (150 mm ) you get 7.5 miles

Ten inch (250 mm)  12.5 miles

If the sensor had been a flat disk 5 mm in diameter, it would be pretty much a wash if the sensor is placed 30 mm in front of the focal point to 30 mm behind.  All the light would fall on the sensor, assuming correct alignment.  If you look at the numbers for such a system, you might even find that the directionality is less critical if the sensor is at, or near, focus.

With a sensor with its own optics, such as a phototransistor, things get messy (complicated).  It is not that you cannot use them, you may have to accept some of the inefficiency of placing the sensor off focus to get it to perform in a way that you understand.

Note also that I have used a lens with single focal point, optically ideal.  At least the area of confusion at the stated focal length is much much smaller than the sensor.  That is unlikely to be true for a Fresnel lens.  I know they are affordable for large aperture optics, but they are really sloppy lenses.  Understand their limitations when you try to estimate performance.

By the way, an 8X10 Fresnell can at best perform only slightly better than a ten inch telescope.

I hope this helps.

Best wishes.

James
 n5gui