dispersion ↑↓ thickness correlation

[Becko]

Hi,
We know that on paper ABBE number describes amount of dispersion. But this is not inherited property of a real lens - in a real lens, in order to describe dispersion, we have to include another factor - thickness. The wider the angle of a prism => the more dispersion.

So I wonder how much the less thickness will reduce the negative effect of lower ABBE on a higher refractive index lens.
And before I start digging forgotten formulas, does anyone have some already calculated conclusion?

[drk]

FACT: The refractive effect of the material on the central wavelengths (yellow colors) is the same in principle (though not degree, due to energy differences) as the effect of the peripheral wavelengths (blue, red).

THEREFORE: If you get to go "thinner" via a more optically dense material because you can focus the yellow wavelength more efficiently, then you are stuck with more efficient dispersion (which is just focusing, too) of the reds and blues.

CONCLUSION: They're inextricably linked...thickness, or dispersion. You choose.

CAVEAT: (Having said that, there seems to be some ability to nibble around the edges with different polymers.)

[lensgrinder]

You can approximate the transverse chromatic aberration(TCA) by calculating where you want to calculate the TCA.
For example you could calculate a +5.00, 15mm from center in a material of 1.6 with a v-value of 36. This would give us:

P = 1.5 X 5
P = 7.5

TCA = 7.5/36
TCA = 0.21

It is important to note that generally the TCA cut-off is around 0.10 D

Below is a link for the calculations to calculate the lens with any amount of thickness using the same +5.00 with a center of 4.6 and a -5.00 with a center of 1.5 in 1.6 material, I calculated using a 30 degree eye rotation and a 12mm vertex.

https://www.mccardle.me/analysis/Abbe-ray-trace.pdf

https://www.mccardle.me/analysis/

[Robert Martellaro]

Hi,
We know that on paper ABBE number describes amount of dispersion. But this is not inherited property of a real lens - in a real lens, in order to describe dispersion, we have to include another factor - thickness.

I'm not aware of any direct correlation between thickness and dispersion, at least with ophthalmic lenses.

Generally, higher refractive index lenses have greater levels of dispersion.

The wider the angle of a prism => the more dispersion.

Perhaps you mean the greater the value of prism (induced or prescribed) the greater the value of chromatic aberration?

Best regards,

Robert Martellaro

[lensgrinder]

I'm not aware of any direct correlation between thickness and dispersion, at least with ophthalmic lenses.

Generally, higher refractive index lenses have greater levels of dispersion.

Perhaps you mean the greater the value of prism (induced or prescribed) the greater the value of chromatic aberration?

Best regards,

Robert Martellaro

As the thickness increases the prism amount increases thereby increasing the transverse chromatic aberration viewed by the wearer.
The prism looking 30 degrees away from center in a +5.00 with a 4.2 mm center will give you 8.23 D of prism and 0.20 D of TCA, this same lens with a center of 5.2 mm will give you 8.48 D of prism and 0.21 D of TCA.

[Robert Martellaro]

As the thickness increases the prism amount increases thereby increasing the transverse chromatic aberration viewed by the wearer.
The prism looking 30 degrees away from center in a +5.00 with a 4.2 mm center will give you 8.23 D of prism and 0.20 D of TCA, this same lens with a center of 5.2 mm will give you 8.48 D of prism and 0.21 D of TCA.

Brent,

The formulas I've seen make no mention of thickness, but then at our level (ophthalmic dispensing) .01∆ of Transverse Chromatic Aberration is, practically speaking, inconsequential (apparently not for post grad differential geometry mathematician types though).

https://www.optiboard.com/forums/showthread.php/5874-Abbe-Value?p=45680&viewfull=1#post45680

Note: Lateral and transverse chromatic aberration are the same.

Best regards,

Robert Martellaro

[lensgrinder]

Brent,

The formulas I've seen make no mention of thickness, but then at our level (ophthalmic dispensing) .01∆ of Transverse Chromatic Aberration is, practically speaking, inconsequential (apparently not for post grad differential geometry mathematician types though).

https://www.optiboard.com/forums/showthread.php/5874-Abbe-Value?p=45680&viewfull=1#post45680

Note: Lateral and transverse chromatic aberration are the same.

Best regards,

Robert Martellaro

The formulas remain the same: TCA = P/v

The difference is in how you determine prism amount. Using Prentice's rule you do not take the the angle of incidence and refraction from both surfaces into account. From these values you can determine the angle of deviation and then prism using P = 100[tan(d)]

From the earlier example a +5.00 viewed 14mm from center(~30 degrees) will exhibit 7 D of prism, but the actual prism value is 8.23 D.
TCA = 7/41 = 0.17 D

Either way, I agree with you, we are splitting hairs and 0.01 or 0.04 does not make much of a difference.

[Uilleann]

Oh I love these sort of discussions! Mostly because I always learn cool new facts and tricks - but also cause it shreds the poly haters...with SCIENCE!

[Robert Martellaro]

The formulas remain the same: TCA = P/v

The difference is in how you determine prism amount. Using Prentice's rule you do not take the the angle of incidence and refraction from both surfaces into account. From these values you can determine the angle of deviation and then prism using P = 100[tan(d)]

From the earlier example a +5.00 viewed 14mm from center(~30 degrees) will exhibit 7 D of prism, but the actual prism value is 8.23 D.
TCA = 7/41 = 0.17 D

Either way, I agree with you, we are splitting hairs and 0.01 or 0.04 does not make much of a difference.

Yup, Prentice's rule is not dead-on balls accurate for oblique angles of view, and certainly doesn't take into account higher orders of aberration (3rd?), just as best form theory breaks down over +8.00 D without asphericity. In fact, most of our formulas rely on small angle approximations. Moreover, Remole's equations demonstrate how steeper values for base curves strongly effects prismatic deviations, at least when compared to Prentice's equation.

Most of this stuff is for lens designers, but some of it is useful when the going gets tough out in the field.

Best regards,

Robert Martellaro

[Becko]

Thanks everyobody for sharing knowledge.
I enjoyed the 'war between optics and cosmetics' that has all the info I need, except it's for 2mm center thickness. My question is how much chromatic aberrations would you have in, for example, 1.6 with 1mm center thickness.
Someone told me I could put all data into Beam4 and see what happens, so currently I'm reading the manual of this rather complicated software.

[Becko]

Some advancement on the topic but I need to gather more data. I actually realized something that completely changes my understanding of Abbe, but I have to make many calculations trying to prove it wrong, in order to have a conclusion and share with everyone.

In the meantime does anyone have some data about materials to share with me, so I can feed the software?
I need index for D, F and C rays for cr39, 1.6 (no idea which 1.6 exaclty different companies use), 1.67 and 1.74. Poly was built in the software for some reason..

Thanks in advance!

[Lelarep]

Some advancement on the topic but I need to gather more data. I actually realized something that completely changes my understanding of Abbe, but I have to make many calculations trying to prove it wrong, in order to have a conclusion and share with everyone.
In the meantime does anyone have some data about materials to share with me, so I can feed the software?
I need index for D, F and C rays for cr39, 1.6 (no idea which 1.6 exaclty different companies use), 1.67 and 1.74. Poly was built in the software for some reason..

Thanks in advance!

You're trying to prove your understanding is wrong, or that ABBE is wrong, which really would be something.

[Becko]

lol, kinda both..
I'm trying to prove myslef wrong, to see if I'm right.
I'm also trying to show how Abbe is an 'abstract' number, especially if you don't know what to do with it. Kind of like Dk and Dkt for contact lenses.

[Becko]

Help!
I wrote a few companies and noone knows or wants to share such info.
I need refractive index for 3 colors in all materials. Any lens producers here?

Please fill https://docs.google.com/spreadsheets...it?usp=sharing