[pure-silver] Re: <somewhat OT> New lens design technology
- From: "Peter Badcock" <peter.badcock@xxxxxxxxx>
- To: pure-silver@xxxxxxxxxxxxx
- Date: Fri, 2 Feb 2007 16:53:55 +1100
On 02/02/07, Sauerwald Mark <mark_sauerwald@xxxxxxxxx> wrote:
That is true, but for a conventional lens there is a limit to the diameter
that you can make a lens and still maintain a given focal length, with this
arrangement, there is not a limit - as the disk gets larger, you have more
internal reflecting surfaces (those would be equivanent to the elements in a
conventional lens), and the aperture would grow as the square of the
diameter - so a larger lens gets more and more light gathering capability.
Assume for the moment that the air-glass interface losses are 0% (realistic
values are dealt with in my next paragraph), then in order for an Origami
lens to achieve the same light gathering power as traditional multi-element
lens, it would need to have approx TWICE its diameter!! [1] OK so perhaps
that is not a big deal in the applications mentioned (such as surveillance
aircraft, cell phones and infrared night vision applications where the
lenses are already small in diameter), but it would take some getting used
to if I had to replace my 62mm diameter (f=35-135mm) lens for my 35mm film
camera with a lens that is 112mm in diameter !
Also, in a conventional lens, there is a fairly large amount of light loss
from passing through the air-glass surface, in this case the entire light
path is within one piece of glass, so those losses should be minimal - think
of how many internal reflections light has when travelling through a piece
of fiber optic cable.
The light losses are not that great. In fact in a hypothetical 6 element
lens using efficient antireflective
coating<http://www.globalspec.com/FeaturedProducts/Detail/JMLOpticalIndustries/Antireflective_Coatings_for_Efficient_Transmission/27932/1>,
only 3% of the light would be lost to internal reflections.
regards
Peter
[1]
Looking at this
<http://www.jacobsschool.ucsd.edu/uploads/news_release/2007/light_path.jpg>detailed
picture of the Origami lens, I estimate that the width of the
circumferential annulus is 5mm when the diameter is 60mm. Preserving that
ratio means that the annulus width is 1/6th the radius length.
Therefore the annulus' surface area, Ao = PI *((Ro)^2 - (Ro*5/6)^2)
where Ro=radius of Origami lens and Ao=Area of Origami's annulus.
Let surface area of traditional multi-element lens, At = PI * (Rt)^2
For equivalent light gathering power, set At=Ao and solve for Ro as a
function of Rt
therefore PI * (Rt)^2 = PI *((Ro)^2 - (Ro*5/6)^2)
therefore (Rt)^2 = (9/36)* (Ro)^2
therefore Rt = [sqrt(11)/9]* Ro
therefore Rt ≈ 0.55* Ro
hence Ro ≈ 1.8 * Rt
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