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.

Leur compréhension est utile pour un optométriste.

Le texte est en anglais ,  extrait du brevet original de Humphrey de 1979.

 

Les quatre faisceaux sont créés par des diodes émettant une lumière de couleur rouge.

 

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Referring to FIG. lb, suspect optics S1 are shown in the form of a spherical lens S1.

If the spherical lens S1 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.)

 

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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.

Cross cylinder lenses can vectorially add.
 
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, Xi,Yi are the deflections of light ray i.

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. 
Humphrey  has  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.