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Date: 01 Aug 2007 20:28:42
From: Protagonist
Subject: Lens makers formula for spherometer
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I have a spherometer, 3 point with 1/4" balls, but i don't have a manual
how to use it.
Is there any lens makers formula, to calculate the measurement including
the spherical, arc-to-arc tangency points included from the 1/4" balls?
Thx!
JS
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Date: 02 Aug 2007 00:07:27
From: Richard F.L.R.Snashall
Subject: Re: Lens makers formula for spherometer
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Protagonist wrote:
> I have a spherometer, 3 point with 1/4" balls, but i don't have a manual
> how to use it.
> Is there any lens makers formula, to calculate the measurement including
> the spherical, arc-to-arc tangency points included from the 1/4" balls?
> Thx!
> JS
Just pretend it's not there and take it away at the last minute. If the
surface is concave, subtract the radius of the balls from the determined
surface radius. If the surface is convex, add it, instead.
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Date: 01 Aug 2007 21:29:27
From: Protagonist
Subject: Re: Lens makers formula for spherometer
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Richard F.L.R.Snashall wrote:
> Protagonist wrote:
>> I have a spherometer, 3 point with 1/4" balls, but i don't have a
>> manual how to use it.
>> Is there any lens makers formula, to calculate the measurement
>> including the spherical, arc-to-arc tangency points included from the
>> 1/4" balls?
>> Thx!
>> JS
>
> Just pretend it's not there and take it away at the last minute. If the
> surface is concave, subtract the radius of the balls from the determined
> surface radius. If the surface is convex, add it, instead.
Found this:
http://historydb.adlerplanetarium.org/dioptrice/?details=1;page=measuring
Scroll down to "Ball spherometer method"!
# Ball spherometer method
To reduce wear on the sharp edge of the ring and to protect the optics
an alternative is a ring with three small ball bearings of diameter d
embedded in it at 120° angles. The centers of the balls define a circle
of radius a and as for the ring spherometer, the sagitta is s. Then the
curvature and radius of curvature of the lens surface are given by C =
1/R = 2s/(a2 + s2 - sd). In the equation, s is taken as positive for a
convex surface and negative for a concave surface.
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Date: 02 Aug 2007 01:04:04
From: Richard F.L.R.Snashall
Subject: Re: Lens makers formula for spherometer
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Protagonist wrote:
> Richard F.L.R.Snashall wrote:
>
> To reduce wear on the sharp edge of the ring and to protect the optics
> an alternative is a ring with three small ball bearings of diameter d
> embedded in it at 120° angles. The centers of the balls define a circle
> of radius a and as for the ring spherometer, the sagitta is s. Then the
> curvature and radius of curvature of the lens surface are given by C =
> 1/R = 2s/(a2 + s2 - sd). In the equation, s is taken as positive for a
> convex surface and negative for a concave surface.
In other words, R = [( a2 + s2 ) / 2s] - d/2!
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Date: 02 Aug 2007 00:44:27
From: Protagonist
Subject: Re: Lens makers formula for spherometer
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Richard F.L.R.Snashall wrote:
> Protagonist wrote:
>> Richard F.L.R.Snashall wrote:
>
>>
>> To reduce wear on the sharp edge of the ring and to protect the optics
>> an alternative is a ring with three small ball bearings of diameter d
>> embedded in it at 120° angles. The centers of the balls define a
>> circle of radius a and as for the ring spherometer, the sagitta is s.
>> Then the curvature and radius of curvature of the lens surface are
>> given by C = 1/R = 2s/(a2 + s2 - sd). In the equation, s is taken as
>> positive for a convex surface and negative for a concave surface.
>
> In other words, R = [( a2 + s2 ) / 2s] - d/2!
Aperantly, curvature C is 1/R. What ever it means!
I'm out of math a long time now.
JS
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Date: 01 Aug 2007 21:23:58
From: Protagonist
Subject: Re: Lens makers formula for spherometer
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Richard F.L.R.Snashall wrote:
> Protagonist wrote:
>> I have a spherometer, 3 point with 1/4" balls, but i don't have a
>> manual how to use it.
>> Is there any lens makers formula, to calculate the measurement
>> including the spherical, arc-to-arc tangency points included from the
>> 1/4" balls?
>> Thx!
>> JS
>
> Just pretend it's not there and take it away at the last minute. If the
> surface is concave, subtract the radius of the balls from the determined
> surface radius. If the surface is convex, add it, instead.
May be OK for mirrors, but not for highly accurate lenses.
JS
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