BEst form spherical lens formula

[ioptic]

Hi all,

I am getting to old to rember the formula for the best lens form.
Zeiss used to go on and on about it.

It works out the ideal F1 cuve for a given power, in order to minimise the sperical aberations caused by the Rx power.

I could probably find it in one of my old text books- if I could only find the books etc... :)

But ime hase moved on- perhaps we have a better way to get the best curve.

thanks all
rOb
-o-o-

[rbaker]

Corrected curve lens theory can best be researched through the works of Dr. Edgar Tillyer of American Optical

http://www.dickwhitney.net/AOHistoryLensDesigners.html

and Bauch & Lomb in the United States

http://www.optics.rochester.edu/

and Carl Zeiss in Germany.

I have a CD with a lot of historical info. Send me your address and I will mail you a copy.

[ioptic]

Hi Dick,

thanks- that was a lot of interesting information!

thanks and best regards
ROb
-o-o-

[tmorse]

Hi all,

I am getting to old to rember the formula for the best lens form.
Zeiss used to go on and on about it.

It works out the ideal F1 cuve for a given power, in order to minimise the sperical aberations caused by the Rx power.

You might also Goggle 'Vogel's Formula'. It's a formula for base curve selection that will minimize two (2) of the most important lens aberrations... 'marginal astigmatism' and 'curvature of field'. Spherical aberration is not one of them, so I suggest you dig out your textbook.;)

[HarryChiling]

Vogels is a good rule of thumb, but it doesn't apply to mid to high index lenses or vertex distances outside the norm, for a more detailed table you an download this excel sheet that uses a more accurate formula which either sets the tangetial and sagittal powers equal to each other "zero marginal astigmatism" or eliminates curvatre of field.

http://onlineopticianry.com/wordpress/?p=163

[ioptic]

Hi Harry,

what a neat web site! and fabulous playground for opticians :)

I'll be making it one of my favourite!

many thanks
ROb
-o-o-

[Darryl Meister]

Vogel's formula is a good approximation, but the original "formula" for "best form" lenses was a quadratic equation with two possible answers. A graph of the plus and minus roots of this equation as a function of lens power is known as Tscherning's ellipse. In addition to the excellent information on Harry's site, you can find a continuing education article on lens design at OptiCampus Lens Design Course.

[HarryChiling]

Vogel's formula is a good approximation, but the original "formula" for "best form" lenses was a quadratic equation with two possible answers. A graph of the plus and minus roots of this equation as a function of lens power is known as Tscherning's ellipse. In addition to the excellent information on Harry's site, you can find a continuing education article on lens design at OptiCampus Lens Design Course.

Don't forget to add a component in your Spectacle Optics program. ;)

[ioptic]

Hi Optiformum contributors!

Must say that I am very impressed about the caliper of the contributors and the web-links to the resouces are also top-notch. Well done everyone- I am usually not easily impresssed, but this left me speachless!

Season's greetings
Rob
-o-o-

[Barry Santini]

You might also Goggle 'Vogel's Formula'. It's a formula for base curve selection that will minimize two (2) of the most important lens aberrations... 'marginal astigmatism' and 'curvature of field'. Spherical aberration is not one of them, so I suggest you dig out your textbook.;)

Challenge question: Why would the aberration known as "curvature of field" be significant for the human eye? The retinal plane is curved, is it not?

In telescope design, with which I am familiar, we were, *for visual use*, not too concerned with curvature of field issues from the objective. We would just ensure that the eyepieces we designed had a *matching* curvature of field, and there would be no edge-of-field defocus apparent to the viewer.

Matching focal plane curvatures is what we are after, or at least *not* mismatching them.

FWIW

Barry

PS - The above did not apply to scopes that were used with film/CCDs. They obviously require demand a flat focal plane.

[Darryl Meister]

In spectacle lenses, curvature of the field is generally calculated as the eye looks away from the center of the lens. It is assumed that the principal ray from the object is intersecting the fovea, so the shape of the actual imaging surface of the eye (or retina) doesn't really matter, unless you're attempting to calculate the curvature of the field error for the eye, itself.

Also keep in mind that visual acuity drops off very rapidly away from the fovea, so the eye actually has a relatively narrow range of high-acuity vision across the retina. Consequently, for extremely large or close objects that would actually cover a significant portion of the retina, we do not have the capability to resolve most of the object clearly anyway, without turning our eye at least.

That said, some degree of curvature of the field is necessary, because the eye does rotate, creating an ideal image plane, known as the far-point sphere, which is also curved. In fact, spectacle lenses usually do not produce enough curvature of the field error to maintain clear vision for off-axis viewing angles. The difference between the actual image plane of the lens for off-axis object points and the ideal image plane of the eye (or far-point sphere) is known as power error. With spectacle lenses, you generally need a significant curvature of the field error to obtain zero power error.

[HarryChiling]

Also keep in mind that visual acuity drops off very rapidly away from the retina, so the eye actually has a relatively narrow range of high-acuity vision across the retina. Consequently, for extremely large or close objects that would actually cover a significant portion of the retina, we do not have the capability to resolve most of the object clearly anyway, without turning our eye at least.

Replace that Retina with fovea, if I could also add to that great answer even 5 degrees off from the center of the fovea and VA drops to less than 20/60 out to 35 to 40 degree and we're talking about less than 20/200 vision.

[Darryl Meister]

Good catch, Harry.

[ioptic]

I have thought for some time that astigmatism due to the angle the eye uses, when looking through a lens, is the main cause of blur in the pheriphery. This phenomena can sometimes be found when Mf wearers report no pheripheral sway and clear pheripheral vision- which is at odds with the normal- "clutching anything to steady themselves"- type of a response- many first time wearers have:)... Then a few years later, when the add chages even by 0.25, all hell braeks loose- because the pheriphery is now blured. When measuring the old spec's pheripheral astigmatism caused by the Mf, then comparing it with the new lenses' astigmatism...they then usually differ in axis and strength and location point of astigmatism- relative to the eye... Getting an add that has the same astigmatism in the pheriphery fixed these patients (often with a little more + in the distance etc... makeing then MF's an office type lens etc..).

This is one fo freeforms' unfulfilleld promises- and one day- when I have nothing better to do- i'll do some more research work on this phenomena :)

season's greetings
Rob
-o-o-

Challenge question: Why would the aberration known as "curvature of field" be significant for the human eye? The retinal plane is curved, is it not?

In telescope design, with which I am familiar, we were, *for visual use*, not too concerned with curvature of field issues from the objective. We would just ensure that the eyepieces we designed had a *matching* curvature of field, and there would be no edge-of-field defocus apparent to the viewer.

Matching focal plane curvatures is what we are after, or at least *not* mismatching them.

FWIW

Barry

PS - The above did not apply to scopes that were used with film/CCDs. They obviously require demand a flat focal plane.