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Thread: Converting sags to radii to dioptric powers...

  1. #1
    sub specie aeternitatis Pete Hanlin's Avatar
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    Converting sags to radii to dioptric powers...

    I'm embarrassed to admit that I have some doubt about this matter, but doesn't the dioptric power of a curve (given the radius of curvature) vary depending on the index of the lens being measured?

    For example, say you are given a polycarbonate lens with a sag (at 40mm) of 1.75. The radius of curvature is going to be 114.21mm (or thereabouts). If the lens had an index of 1.53, the dioptric value of that radius of curvature would be 4.64 diopters. However, considering that polycarbonate has an index of 1.586, the lens really has a front curve value of +4.81 Diopters... correct?

    Thanks for your confirmation or refutation.
    Pete Hanlin, ABOM
    Vice President Professional Services
    Essilor of America

    http://linkedin.com/in/pete-hanlin-72a3a74

  2. #2
    Bad address email on file John R's Avatar
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    Confused Lets see

    To find the curve from a radius is..
    index / radius = Dioptre
    so a 114.21 radius will give you in
    523 = 4.57
    586 = 5.13
    but if you then use a sag chart to find the substance @ 60 m/m it comes to the same 4.00
    sag formula is
    index/Dioptre-SQRT((Index/Dioptre)^2-(Dia/2)^2)

  3. #3
    OptiBoardaholic
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    Pete,
    I agree with John's figures (5.13D for the poly). I think that you may have just have pushed a wrong button on the calculator, since the other figure is OK.
    Regards
    Dave

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    RETIRED JRS's Avatar
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    Pete,

    It's some what determined by the device used and the format wanted. Since you used a Essilor 40mm ball-tip gauge - calibrated in 530, the dioptric conversion @ 1.530 (of 1.75 sag) is 4.643 diopters. Or the curve in tool index (US) if you want to call it that.

    To arrive at the 5.13 curve (mentioned above) you take the (index of material -1) / (index of measuring device - 1) * curve at index measured.

    (1.586-1) / (1.530-1) * 4.643 = 5.1335 (curve of lens in it's index)

    Systems to determine the grind curves will work either way - depending on the indices given it to work with.


    PS - go knock on MV's door and borrow some of his books.
    J. R. Smith


  5. #5
    sub specie aeternitatis Pete Hanlin's Avatar
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    Now I see what I did...

    When I compensated for the index of refraction, I divided 1.586/1.530 (I should have divided .586/.530).

    The main point, however (at least I'll make it the main point, cause its the one I was correct on ;) ), is that the dioptric power of the curve DOES depend on the index of refraction. I was so wrapped up in pointing out that radius AND index determine curvature power that I didn't think twice about the conversion formula.

    As it turns out, it is a moot point, because the surface I'm wanting to verify is aspheric...

    Thanks for the info, everyone... next time I'll remember to take away the ones!
    :D
    Pete Hanlin, ABOM
    Vice President Professional Services
    Essilor of America

    http://linkedin.com/in/pete-hanlin-72a3a74

  6. #6
    Master OptiBoarder Darryl Meister's Avatar
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    Hi Pete,

    I'm going to summarize the rest of these very goods posts, and even elaborate a bit, in order to present a bigger picture to some of our less technical visitors.

    Surface power, which is ultimately what we are interested in, is the product of two factors: curvature and refractive index. More specifically, the surface power P is defined as:

    P = Curvature * Delta Index

    where Curvature is the reciprocal of the radius of curvature of the surface in meters and Delta Index is the difference between the refractive index of the material and the refractive index of the surrounding medium (most often air, with an index of 1.000).

    Consequently, surface power is proportional to both the curvature of a lens surface and the difference between the refractive of the lens material and air.

    "Curvature" is a pretty straightforward concept: the steeper something is, the more curvature it has, while the flatter something is, the less curvature it has. For instance, the Earth appears very flat to us because it has very little curvature (or, conversely, a very long radius of curvature). Imagine standing on a basketball, which has a relatively large curvature (or, conversely, a very short radius of curvature), instead of the Earth... You will quickly realize how much more curvature the basketball has as you stumble over it. The unit of curvature is the reciprocal meter, until it is multiplied by a refractive index (or Delta Index), in which case the unit becomes the diopter.

    "Delta Index," or the difference in refractive index between two media, such as air and a lens material, is essentially a measure of how much light will be refracted as it passes from one medium to another. The bigger the difference between refractive indices, the more refraction will occur at the boundary between the two media. Consequently, a 1.66 high-index lens material will produce a bigger Delta Index, and refract light more, than a 1.499 plastic lens material.

    Any device that measures the height (or sagitta) of the surface, such as a lens clock or a sag guage, is actually measuring the curvature of the surface -- not the surface power. To give you results in "diopters of surface power," the device assigns an arbitrary refractive index to the surface power formula above. This arbitary index is usually the standard tooling index of 1.530, so the surface power formula becomes:

    P = Curvature * 0.530

    Note that Delta Index becomes 1.530 - 1.000 (the refractive index of air) = 0.530. Generally, the value for P in this formula should be called something other than surface power, to prevent confusion. "Tool power" or "tool curve" is a little less ambiguous.

    Consequently, whenever you measure the lens surface on a material with a refractive index other than 1.530 using a sag guage, a compensation must be made to determine the actual surface power P from the tool power read from the device. This compensation formula is known as the curve variation factor:

    P = Measured Power * (Actual Index - 1)/(1.530 - 1)

    where Measured Power is the value read from the lens clock or sag guage and Actual Index is the actual refractive index of the lens material.

    Best regards,
    Darryl

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