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Thread: Brain-exploding problem

  1. #1
    What's up? drk's Avatar
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    Brain-exploding problem

    Ok, just for fun, how would this be calculated?

    I just read that with LASIK, for every diopter of myopia corrected, the cornea is thinned by 15 microns (0.0015 M).

    Generally speaking, the cornea is about 550 microns thick, and as you know the central corneal anterior surface radius of curvature is about 43-46 diopters (although I'm not sure if that is a power approximation or the inverse of the radius of curvature in air*). Average corneal size is about 11.5-12 mm.

    So, without the drudgery of doing the problem, what is the correct concept...difference in sagittal depth?

    P.S. Just thought of this...sagitta...Sagittarius...the Archer..."Bow"!

    *Ok, not to bog down, but keratometric measurements are not radii of curvature in air, but power estimations using the simple formula of F = (n'-n)/f. The cornea's refractive index is like water, i.e. 1.33, thus the true radius of curvature of the anterior cornea is more like 0.33/43 to 0.33/46, or 7.7 mm to 7.2.

  2. #2
    ATO Member HarryChiling's Avatar
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    Quote Originally Posted by drk View Post
    I just read that with LASIK, for every diopter of myopia corrected, the cornea is thinned by 15 microns (0.0015 M).
    Your unit is off,(no wise crack funny guy :bbg:) a micron is 1 x 10-6M so 15 microns would be 0.000015M

    Using the example of a schematic eye:

    Anterior Cornea (radius mm) = 7.7mm
    Anterior Cornea (index) = 1.376

    Front Curve Power (D) = (1.376 - 1)/0.0077 = 48.83D

    Anterior Corneal (radius mm) = 6.8mm
    Vitreous (index) = 1.336

    Back Curve Power (D) = (1.336 - 1.376)/0.0068 = -5.88D

    Corneal Thickness (mm) = 0.5mm

    Back Vertex Power of System = -5.88 + [48.83 - (0.0005/1.376)*48.832] = 42.08D

    After a 15 micron change in thickness

    Back Vertex Power of System = -5.88 + [48.93 - (0.000485/1.376)*48.932] = 42.20D

    I only get a 0.12D difference I'm probably doing something wrong, but here's my excell sheet.
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  3. #3
    What's up? drk's Avatar
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    Thanks, Harry.

    Yes, you're right, of course. 1 micron is 1000th of 1000th :o

    You also noted correctly that the index of refraction of the cornea is 1.376, not 1.33 (I've been looking stuff up).

    My source is just "some OD" that was quoted in an article. Maybe he's off.

    What's the sag equation:
    Sagittal depth:

    s = R - sqrt [R squared-(d/2)squared]

    Isn't this the key?

    Wouldn't you plug in a change in R of 1 diopter and note the change in sag depth, assuming a normal corneal diameter?
    Last edited by drk; 04-22-2008 at 10:03 AM.

  4. #4
    ATO Member HarryChiling's Avatar
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    Alright so here's another shot at it.

    If the anterior radius is 7.7mm, the index is 1.376, the diameter 12mm, and were reduceing the sag of the lens by 15 microns then:

    Sag = 7.72 - [7.72 - (12/2)2] = 2.874028595

    Minus the 15 micorns

    2.859028595

    the radius of that sag and a 12mm diameter lens would be:

    Radius = [(2.859028595)2 + 62]/[2*(2.859028595)] = 7.725

    then that radius is equivalent to the dioptric power of:

    Power Before = (1.376 - 1)/0.0077 = 48.83D
    Power After = (1.376 - 1)/0.007725 = 48.67D

    0.16D change

    If we were to plug it through the whole system like in the previous example the back vertex would be:

    Back vertex: 42.11D Compared to 42.08D from the previous example 0.03D change. I attached the file again, I still don't get it but maybe I missed somthing. Does the writer give an example?
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    Most "authorities" quote the cornea at 1.3375
    The old B&L Keratometer is set for1.3375.

    Chip

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    Master OptiBoarder lensgrinder's Avatar
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    What they use in Lasik for Excimer lasers is a formula called the Munnerlyn Formula, named for an engineer named Charles Munnerlyn.


    So assuming an optical zone of 7mm with a one diopter change.

  7. #7
    ATO Member HarryChiling's Avatar
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    Quote Originally Posted by lensgrinder View Post
    What they use in Lasik for Excimer lasers is a formula called the Munnerlyn Formula, named for an engineer named Charles Munnerlyn.


    So assuming an optical zone of 7mm with a one diopter change.
    Nice pull Brent. :cheers:
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  8. #8
    What's up? drk's Avatar
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    If I need optics and I post on the OD message board, I get blank stares.

    You opticians know your optics.

    I tip my cap.

    (Chip, I've since heard that Bausch & Lomb used 1.376 for their Keratometer and the [AO?] Ophthalmometer used 1.3375. Go figure.)
    Last edited by drk; 04-21-2008 at 09:34 PM.

  9. #9
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    Quote Originally Posted by drk View Post
    What's the sag equation:
    Sagittal depth:

    s = R squared- sqrt [R squared-(d/2)squared]
    Minor correction:

    Formula for s = R- sqrt[Rsquared-(d/2)squared]:cheers:

  10. #10
    What's up? drk's Avatar
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    Duly noted.

  11. #11
    ATO Member HarryChiling's Avatar
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    Quote Originally Posted by drk View Post
    If I need optics and I post on the OD message board, I get blank stares.

    You opticians know your optics.

    I tip my cap.

    (Chip, I've since heard that Bausch & Lomb used 1.376 for their Keratometer and the [AO?] Ophthalmometer used 1.3375. Go figure.)
    Our keratometer uses 1.3375 as the index, I just use 337.5/K to get theradius in mm or in reverse to figure the K if I have a mm measure.
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