## Theorie du frontofocometre automatique

Par RLRP le jeudi 7 février 2013, 19:46 - Lien permanent

Les principes théoriques qui régissent le fonctionnement d’un frontofocomètre automatique sont décrits en prenant le cas d’un frontofocomètre Humphrey ( Zeiss )350 ou 360.

Le texte est en anglais

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Referring to FIG. lb, suspect optics S1 are shown in the form of a spherical
lens S1. As is well known in the art, spherical lens S1 will cause light to be
deflected inwardly.

This is shown in FIG. lb with respect to a Cartesian coordinate axis system.
Writing such deflection in an algebraic equation will give the general
expression for spheriçal equivalent (Seq)

Seq= -X1+X2+X3-X4-Y1- Y2+Y3+Y4

where, Xi, Yi are the deflections of light ray i

(For simplicity, a factor of proportionality between sphere power and
deflection has been assumed as unity; hence, does not appear in these
relations.)

Referring attention to FIG. 1c, deflection produced by cross cylinder lenses
is illustrated. Specifically, suspect optics S2 are shown comprising

a positive cylinder 20 aligned along the 90° axis or Y axis and .

a negative cylinder 22 aligned along the 0° axis or X axis .

( Typically, such lens elements are composite and exclude the illustrated
optical interface between them -this interface being shown only for ease of
understanding. )

Adopting the same convention, the 0°-90° cylinder (C+) can be expressed .
.

C+=2(+X1-X2-X3+X4-Y1-Y2+Y3+Y4).

where, Xi,Yi are the deflections of light ray i.

It is known that cross cylinder lenses can vectorially add.

For example, see U.S. Pat. No 3,822,932 issued July 9, 1974, entitled
“Optometric Apparatus and Process Having Independent Astigmatic and Spherical
Inputs.

FIG. 1d illustrates a positive cylindrical lens 24 at 45° of angularity and a
negative cylindrical lens 26 at 135° of angularity. The optical interface
between lenses 24, 26 is shown for ease of understanding only.

Where Cx equals 45°-135° angularity , the algebraic equation for such
deflection may be written

Cx=2(+X1+X2-X3-X4+Y1-Y2-Y3+Y4)

where, the X and Y coordinate deflections are written as before. .

It will be appreciated that the above algebraic expressions when combined
will locate the powers of most eyeglass lenses.

Specifically, sphere, cylinder, cylinder axis will all be a function of the
above-expressed general equations.

However, lenses can be in forms other than sphere, cylinder and prism. If they
are, it is important to be able to know that the lenses are not conventionally
described and alert the operator to this fact.

Such lenses can be generally detected by the following equations:

CA= +X1+X2-X3-X4-Y1+Y2+Y3-Y4

PV1=—Xl+X2-X3+X4—Y1+Y2—Y3+Y4 . .

PV2=+X1—X2+X3—X4—Y1+Y2—Y3+Y4

where, CA is proportional to circular stigmatism, PV1 and PV2 are proportional
to components of power variation across the lens surface. . . .

Regarding circular astigmatism (CA), the refractive vergence resulting from
combining a series sphero-cylinder lenses used in tandem can usually be
adequately expressed in terms of equivalent lens , of some simpler
sphero-cylinder lens . in an appropriate lens plane.

This is possible because a pair of sphere lenses used in tandem can be
expressed as another “effective sphere” by well-known formulae, or a sphere and
cylinder may be similarly “combined” to an equivalent sphere-cylinder using
similar formulae for the appropriate meridians.

However, this convenient equivalent for several lenses used in tandem is not
universally true.

The usual formulae for combining lens effects apply to a pair. of cylinders of
similar oriented axes, to yield a new equivalent lens.

However, cylinder lenses whose axes are not aligned . lead to new optical.
effects not expressible in • terms of simple sphero-cylinder lens effects. The
effects that depart from those generated by conventional lenses will be called
“circular astigmatism.” The size of the effect (circular astigmatism) generated
by a pair of obliquely aligned cylinders is fully comparable to the effects
normally generated by the separation of thin lenses, i.e., the circular
astigmatism is proportional to the powèr of each cylinder and their
separation.

Fortunately, this is usually a small power in the most important case of the
structure of the human eye and can usually be neglected as a factor in human
vision.

Regarding power variations associated with the quantities PV1 and PV2, these
types of lens power variations are illustrated by those lenses shown and
described in U.S. Pat. No. 3,507,565 issued Apr. 21, 1970 to Luis w. Alverez
and WilIiam E Humphrey, entitled “Van.. able Power Lens and System at Selected
Angular Orientations,” and US. Pat. No. 3,751,138 issued Aug. 7, 1973 by
WilIiam E Humphrey, entitled “Variable Astigmatic Lens and Method for
Constructing Lens.”

As will readily be appreciated by those skilled in the optic arts, these lenses
include spherical and cylindrical lens properties which are variable over the
surface of the lens. Additionally, other types of lenses can produce these type
of variable sphere and cylinder powers.

For example, bifocals registered at the optical boundaries so that one lens
registers to at least one aperture and the remaining lens registers to the
remaining apertures can produce such an indication of lens power
variation.

i: have found generally that if multiple

[(S)(CA)]< 0.2

SQRT. [ (PV1)2+ (PV2)](S)) <0.3

then the overall powers of the lens system as measured will not be appreciably
affected. The terms S wiIl be hereinafter described.

It should be appreciated in the above equations, three light beams required to
identify a solution in sphere, cylinder, cylinder axis and prism.

However, determination of power variations (PV), increased data for precision
and checking giving commercial photodetector with four detectors make arrays
preferred.