Base curve - true base curve - refractive index

[dadeppo]

Hello to all,

I need some help in understanding base curve, true base curve, cx radius and refractive index.

Firstly, in theory which is the wavelength at which a +1D lens has to have 1 m focal length (the green mercury line, e 546.07 nm, or the yellow sodium, d 587.56 nm)?

Then, as for the base curve, I thought that:
- base curve is the base curve referred to a 'reference' refraction index of 1.53 or, sometimes, 1.523
- true base curve is the base curve calculated for the actual refractive index of the material the lens is made
- cx is the actual radius of curvature in mm

If you look at:
http://www.zeiss.com/4125682000258738/EmbedTitelIntern/LPG_Gradal_Brevity_167/$File/LPG_Gradal_Brevity_167.pdf
It seems that I have missed something..
They have listed base curve, that I think are referred to the actual refractive index at d light of the material (?), then true base curve refered to n=1.53 and then cx in mm.

Can anyone explain me which is the correct definition for true base curve?
And in which way I can know the real curvature radius in mm of a semi-finished lens claimed, for instance, to be base 8?

Thank you very much in advance!!
:)

[HarryChiling]

Sodium D is the reference, Marked Base or nominal curve is whats on the box and often uses 1.53 as the tool index, true is the base in the material index so that document your looking at is a little confusing.:hammer:

[lensgrinder]

The US and the UK use the helium d- line, same wavelength as you indicated and continental Europe use the mercury e-line, same wavelength as you indicated.

The radius is dependent upon what the refractive index is, so the radius listed is the radius based on the index of 1.67.
The true curve is based on 1.53 index.

So the radius of curvature for an 8.00 D base in material of 1.67 is 79.45 mm as listed. To find the refractive power you would take (1.67-1) / 0.07945 = 8.43 D

[Darryl Meister]

The radius is dependent upon what the refractive index is, so the radius listed is the radius based on the index of 1.67.
This might be a little confusing. The radius actually represents the physical curvature of the lens surface, and is therefore independent of refractive index. However, if you are trying to achieve a specific surface power, you would need to alter the radius in order to account for the increase or decrease in power due to the refractive index.

Lensgrinder's description of the "true curve" is correct though; it represents the 1.530-based surface power or "tooling power" of the surface,

True Curve = 530 / Radius

Unless the material actually has a 1.530 index of refraction, the true curve will not represent the actual refractive power of the surface. However, use of a single reference or "tooling" index simplifies things somewhat, particularly when dealing with sag gauges that can only be calibrated in one refractive index, the possibility of different reference wavelengths, and so on.

Lensgrinder's description of the Helium d and Mercury e reference wavelengths is also correct. As Harry indicated, the "marked" or "nominal" curve represents how manufacturers label the lens blanks; often, they are simply rounded true curve values. They generally don't represent any real surface quantity. However, many years ago, the nominal Base curve could represent the power to use for surfacing in order to reduce calculations; this nominal -- or "compensated" -- curve differed from the actual surface power enough to compensate for the gain in Plus power caused by the lens thickness.

[dadeppo]

True Curve = 530 / Radius

Unless the material actually has a 1.530 index of refraction, the true curve will not represent the actual refractive power of the surface.

Thanks to all!!

So that is the definition of the true base curve for manufacturer, using grinding tools and n=1.53, while from the point of view of the optician the true base is the actual base referred to the material index . :)

Just to summarize, if I want to know the actual radius of curvature in mm of a semi-finished lens, in case it's not stated by the manufacturer, I cannot use the claimed base, because it could be only a label..
but, if I have the 'manufacturer' true base expressed at n=1.53, I can find the radius

Radius = 530/ true curve

and then the actual base curve at n (true base for the optician!)

actual base=(n-1)*1000/Radius.

You are also telling me, that the manufacturers usually take into account the nominal power variation versus index, and a n=1.5 'base 8' lens will have a cx around 66 mm, while a 1.67 'base 8' lens a cx around 80 mm..
so that saying 'base 8 lens' never states a predefined curvature radius in mm (??)

Any of you knows what are the expected tolerance on curvature radius manufacturing?

Thank you!!

[Darryl Meister]

so that saying 'base 8 lens' never states a predefined curvature radius in mm (??)
Manufacturers in the US quote Base curve values based on that standard 1.53 refractive index, so an '8 Base' would generally have the same physical curvature, regardless of the actual refractive index. However, the actual surface power of that lens blank would vary with the index.

Any of you knows what are the expected tolerance on curvature radius manufacturing?
You generally won't see tolerances on the radius, since the errors are non-linear; that is, a small error in radius for a 2.00 Base would represent a small change in surface power, while that same error in radius for a 10.00 Base would represent a very large change in surface power. Manufacturers generally adhere to ISO 10322 surface power tolerances or better.