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Thread: resolving oblique astigmatism into V & H components.

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    Confused resolving oblique astigmatism into V & H components.

    It has been a while since I have done this stuff, but I am writing some exams on dispensing and have forgotten some basic trig.
    When resolving oblique astig into vertical and horizontal components do I use Sin (angle of astigmatism) times the power of the cyl for the vertical, and sin (90 - angle of astigmatism)times power for the horizontal.
    Or have I just gone NUTS!!

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    ATO Member HarryChiling's Avatar
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    Thanks!

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    Master OptiBoarder Darryl Meister's Avatar
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    Harry, you may also consider adding the individual formulas for vertical (D90) and horizontal (D180) power:



    and



    where DS is the sphere power, DC is the cylinder power, and a is the cylinder axis.
    Darryl J. Meister, ABOM

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    ATO Member HarryChiling's Avatar
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    Quote Originally Posted by Darryl Meister View Post
    Harry, you may also consider adding the individual formulas for vertical (D90) and horizontal (D180) power:



    and



    where DS is the sphere power, DC is the cylinder power, and a is the cylinder axis.
    I added and then removed that. I thought it was interesting that the person wrote sin(90 - angle of astigmatism) instead of cos(angle).
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    Wink

    I thought it was interesting that the person wrote sin(90 - angle of astigmatism) instead of cos(angle). 08-29-2008 08:49 PM
    "the person" thats me!! was sitting front of page with a triangle trying to remember if adjacent over hypotenuse or opposite over hyptonuse was sin or cos!! This is difficult for us mere optoms. All I know is "whether its better with one or two...."

    Thanks for your help guys. This will make life a lot easier!!

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    Master OptiBoarder Darryl Meister's Avatar
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    "the person" thats me!! was sitting front of page with a triangle trying to remember if adjacent over hypotenuse or opposite over hyptonuse was sin or cos!! This is difficult for us mere optoms. All I know is "whether its better with one or two...."
    No worries. They're easy to forget if you're not working with this stuff on a regular basis.

    On an interesting side-note (or at least a side-note interesting to about five of us on OptiBoard), the specific relationship between the power of a sphero-cylindrical surface and the cylinder axis is derived from a relationship in differential geometry known as Euler's Curvature Formula:



    where k1 and k2 are the "principal" or minimum and maximum curvatures, corresponding to the sphere and cylinder meridians of the lens surface. When the angle (theta) is at 0 degrees, or the axis meridian of the sphere, the cosine-squared term reduces to 1 and the sine-squared term reduces to 0, and vice versa when the angle is at 90 degrees, or the power meridian of the cylinder.
    Darryl J. Meister, ABOM

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    ATO Member HarryChiling's Avatar
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    Quote Originally Posted by Darryl Meister View Post
    No worries. They're easy to forget if you're not working with this stuff on a regular basis.

    On an interesting side-note (or at least a side-note interesting to about five of us on OptiBoard), the specific relationship between the power of a sphero-cylindrical surface and the cylinder axis is derived from a relationship in differential geometry known as Euler's Curvature Formula:



    where k1 and k2 are the "principal" or minimum and maximum curvatures, corresponding to the sphere and cylinder meridians of the lens surface. When the angle (theta) is at 0 degrees, or the axis meridian of the sphere, the cosine-squared term reduces to 1 and the sine-squared term reduces to 0, and vice versa when the angle is at 90 degrees, or the power meridian of the cylinder.
    That formula is used in many forms in our field for instance determining cylinder with a lens clock, adding oblique cylinders.
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    Thanks again. I had got the entire thought process incorrect. I was trying to use basic Pythagoras' theorem to work out the power much like you would with compounding prism.

    Have the equation saved on my desktop so I dont forget.

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