Reconciling the Thick Lens Model with P2P Optical Bench

Started 4 months ago | Discussions
Garry2306 Regular Member • Posts: 108
Reconciling the Thick Lens Model with P2P Optical Bench

As we we know, short of being the lens designer, with full access to optical CAD models etc, The PhotonsToPhotos Optical Bench (OB) is the 'best' insight we have to understanding our lenses: thank you Bill.

At the other extreme we have the Thin Lens model.

Slightly better than the Thin Lens Model is the Split or Thick Lens Model, where we insert a 'pseudo hiatus', which in this post I'll call t.

The Thick Lens Model gives us the following equation: x = (1+1/m)f + t + (1+m)f

Where x is the object to sensor plane distance, m the magnification, and f the focal length.

In the Thick Lens Model the front principal (H) is positioned at (1+1/m)*f from the object and the rear principal (H') at (1+m)f from the sensor.

The hiatus (t) being given by x - (f(1+m)^2)/m

Now the problem/challenge/confusion...at least in my mind.

How to reconcile the Thick Lens Model to the data in the OB?

As an example, let's take the Canon 100mm 2.8 L Macro and use the OH data at the maximum mag, ie minimum focus. The OB gives us the following: m = 1, x = 134.76 + 162.91 = 297.67 (pretty close to the Canon's stated MFD of 300mm.

The OH gives the hiatus at the max mag, ie min focus, as 14.92-13.25 = 1.67.

If we use the Thick Lens Model to estimate t, using the OB value for x (ie 297.91), we get a value of t of 297.91-(100*(1+1)^2)/1 = -102.09

Clearly a large difference between the two models: OB vs Thick Lens

However, if I use the OB value for f at the max mag, ie 74, we get the 'correct' value for t, is the Thick Lens Model and the OB are essentially the same.

So, my question is this: how do I 'adjust' the standard thick lens model to better represent the lens as captured in the OB?

How do I adjust f from 100 to 74? Is there a simple factor to be used, eg like the bellows factor?

BTW it's clearly not the bellows factor (1+m/p) as this would give (1+1/0.28) = 4.57

Bottom line: Should I 'just' accept the thick lens model and stop trying to model the OB with it? Or am I missing a trick in the thick lens model and not correctly using f

alanr0 Senior Member • Posts: 2,485
Re: Reconciling the Thick Lens Model with P2P Optical Bench
4

Garry2306 wrote:

As we we know, short of being the lens designer, with full access to optical CAD models etc, The PhotonsToPhotos Optical Bench (OB) is the 'best' insight we have to understanding our lenses: thank you Bill.

At the other extreme we have the Thin Lens model.

Slightly better than the Thin Lens Model is the Split or Thick Lens Model, where we insert a 'pseudo hiatus', which in this post I'll call t.

The Thick Lens Model gives us the following equation: x = (1+1/m)f + t + (1+m)f

Where x is the object to sensor plane distance, m the magnification, and f the focal length.

In the Thick Lens Model the front principal (H) is positioned at (1+1/m)*f from the object and the rear principal (H') at (1+m)f from the sensor.

The hiatus (t) being given by x - (f(1+m)^2)/m

<snip>

Bottom line: Should I 'just' accept the thick lens model and stop trying to model the OB with it? Or am I missing a trick in the thick lens model and not correctly using f

I have not worked through your calculation in detail, but you seem to be looking for a single model to predict macro performance as focus is adjusted.

The "thick lens" model follows from Gaussian optics results for paraxial imaging, which enable one to ray trace and calculate image and object positions if one knows only the positions of four cardinal points of the lens. Wikipedia: Cardinal points.

This assumes that the optical arrangement is fixed.  It works perfectly if you mount a lens in a bellows and use the bellows to focus images at different object distances.

All bets are off if you re-arrange the glassware between comparisons.  The Canon 100 mm f/2.8 lens relies on internal focussing.  When you focus the lens, effective focal length, principal plane locations and principal plane separation (hiatus) will all change.

For each focus position, Bill's optical bench gives you the effective focal length and principal plane locations, so a new thick lens model for each focus setting.

For an arbitrary lens design, I am not aware of a reliable way to predict how these model parameters will change with focus, other than measurement or modelling of the configuration.  It depends entirely on how each individual lens is constructed.

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Alan Robinson

OP Garry2306 Regular Member • Posts: 108
Re: Reconciling the Thick Lens Model with P2P Optical Bench

Alan

Thanks for the response, BTW I was not thinking about macro, I just ‘randomly’ chose the Canon macro lens as Bill has focus control on this one

I know I’m looking at a lost cause.

Bottom line: I’ll carry on using my DOFIS model, eg https://photography.grayheron.net/2020/12/lens-simulator.html, as a reasonable model when undertaking in camera focus bracketing using Magic Lantern or CHDK Lua scripts.

BTW I always smile when I read some talking about the importance of the circle of confusion when deriving DoF, but ignoring the pupil mag and the distance uncertainty, ie when you don’t know the location of the front principal or entrance pupil as focus varies.

Mark Scott Abeln
Mark Scott Abeln Forum Pro • Posts: 18,154
Re: Reconciling the Thick Lens Model with P2P Optical Bench

It's not just macro photography.

Internal focus lenses—from what I understand—change in focal length with focus, even for non-macro photography. In some lenses this effect is quite strong, even for portrait photography, and is quite obvious.

 Mark Scott Abeln's gear list:Mark Scott Abeln's gear list
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OP Garry2306 Regular Member • Posts: 108
Re: Reconciling the Thick Lens Model with P2P Optical Bench

Mark Scott Abeln wrote:

It's not just macro photography.

Internal focus lenses—from what I understand—change in focal length with focus, even for non-macro photography. In some lenses this effect is quite strong, even for portrait photography, and is quite obvious.

Mark

Yes I understand that, what I was trying to do was to see if I could get a ‘better’ match between the split, thick lens model and the ‘CAD model’. 
As I said, I stick with what I’ve got

bclaff Forum Pro • Posts: 12,453
Re: Reconciling the Thick Lens Model with P2P Optical Bench

Garry2306 wrote:

As we we know, short of being the lens designer, with full access to optical CAD models etc, The PhotonsToPhotos Optical Bench (OB) is the 'best' insight we have to understanding our lenses: thank you Bill.

You are welcome.

...

The Thick Lens Model gives us the following equation: x = (1+1/m)f + t + (1+m)f

Where x is the object to sensor plane distance, m the magnification, and f the focal length.

Sure. I use 'i' for internodal as opposed to 't'

...

The hiatus (t) being given by x - (f(1+m)^2)/m

Sure solving the above for 't'

...How to reconcile the Thick Lens Model to the data in the OB?

As an example, let's take the Canon 100mm 2.8 L Macro and use the OH data at the maximum mag, ie minimum focus. The OB gives us the following: m = 1, x = 134.76 + 162.91 = 297.67 (pretty close to the Canon's stated MFD of 300mm.

FWIW, actually looks like 134.01mm + 162.91mm = 296.92mm

The OH gives the hiatus at the max mag, ie min focus, as 14.92-13.25 = 1.67.

Right. Here's a screenshot for those trying to follow the values (see the Positions line):

Or play with it yourself at Canon EF100mm f2.8L Macro IS USM

If we use the Thick Lens Model to estimate t, using the OB value for x (ie 297.91), we get a value of t of 297.91-(100*(1+1)^2)/1 = -102.09

Clearly a large difference between the two models: OB vs Thick Lens

However, if I use the OB value for f at the max mag, ie 74, we get the 'correct' value for t, is the Thick Lens Model and the OB are essentially the same.

You have discovered the obvious, you don't use f at infinity to calculate t at MFD, for that you need f at MFD.

So, my question is this: how do I 'adjust' the standard thick lens model to better represent the lens as captured in the OB?

No adjustment is necessary just realize that f (almost always) changes as you focus.

How do I adjust f from 100 to 74? Is there a simple factor to be used, eg like the bellows factor?

BTW it's clearly not the bellows factor (1+m/p) as this would give (1+1/0.28) = 4.57

Right. It's not the bellows factor. Lenses are complicated and focal length as you focus closer than infinity (or even exact values at infinity) are not obvious.
One real practical use of the Optical Bench is to get focal length and pupil magnification particularly at higher magnifications.

(Of course focal length can be measured for interchangeable lenses with extension tubes.)

Bottom line: Should I 'just' accept the thick lens model and stop trying to model the OB with it? Or am I missing a trick in the thick lens model and not correctly using f

I think your only "hang up" is trying to use focal length at infinity in non-infinity scenarios.

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Bill ( Your trusted source for independent sensor data at PhotonsToPhotos )

bclaff Forum Pro • Posts: 12,453
Animation of H and H'

BTW, it's fun to turn on Principals and use the Play button when Focus is selected to watch how H and H' behave.

View as :original size" to see the animation

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Bill ( Your trusted source for independent sensor data at PhotonsToPhotos )

OP Garry2306 Regular Member • Posts: 108
Re: Reconciling the Thick Lens Model with P2P Optical Bench

bclaff wrote:

Garry2306 wrote:

As we we know, short of being the lens designer, with full access to optical CAD models etc, The PhotonsToPhotos Optical Bench (OB) is the 'best' insight we have to understanding our lenses: thank you Bill.

You are welcome.

...

The Thick Lens Model gives us the following equation: x = (1+1/m)f + t + (1+m)f

Where x is the object to sensor plane distance, m the magnification, and f the focal length.

Sure. I use 'i' for internodal as opposed to 't'

...

The hiatus (t) being given by x - (f(1+m)^2)/m

Sure solving the above for 't'

...How to reconcile the Thick Lens Model to the data in the OB?

As an example, let's take the Canon 100mm 2.8 L Macro and use the OH data at the maximum mag, ie minimum focus. The OB gives us the following: m = 1, x = 134.76 + 162.91 = 297.67 (pretty close to the Canon's stated MFD of 300mm.

FWIW, actually looks like 134.01mm + 162.91mm = 296.92mm

The OH gives the hiatus at the max mag, ie min focus, as 14.92-13.25 = 1.67.

Right. Here's a screenshot for those trying to follow the values (see the Positions line):

Or play with it yourself at Canon EF100mm f2.8L Macro IS USM

If we use the Thick Lens Model to estimate t, using the OB value for x (ie 297.91), we get a value of t of 297.91-(100*(1+1)^2)/1 = -102.09

Clearly a large difference between the two models: OB vs Thick Lens

However, if I use the OB value for f at the max mag, ie 74, we get the 'correct' value for t, is the Thick Lens Model and the OB are essentially the same.

You have discovered the obvious, you don't use f at infinity to calculate t at MFD, for that you need f at MFD.

So, my question is this: how do I 'adjust' the standard thick lens model to better represent the lens as captured in the OB?

No adjustment is necessary just realize that f (almost always) changes as you focus.

How do I adjust f from 100 to 74? Is there a simple factor to be used, eg like the bellows factor?

BTW it's clearly not the bellows factor (1+m/p) as this would give (1+1/0.28) = 4.57

Right. It's not the bellows factor. Lenses are complicated and focal length as you focus closer than infinity (or even exact values at infinity) are not obvious.
One real practical use of the Optical Bench is to get focal length and pupil magnification particularly at higher magnifications.

(Of course focal length can be measured for interchangeable lenses with extension tubes.)

Bottom line: Should I 'just' accept the thick lens model and stop trying to model the OB with it? Or am I missing a trick in the thick lens model and not correctly using f

I think your only "hang up" is trying to use focal length at infinity in non-infinity scenarios.

Bill

Thanks for taking the time to write that.

I fear I need to stop looking for a ‘better way’ than my current approach, as I just don’t have better numbers. 
For instance, the hub ‘only’ gives data for, say, the EF-M 11-22 at infinity. 
So, other than measuring things myself, which is not going to happen, I’ll pragmatically carry on using the split/thick lens model, based on the manufacturer’s MFD, infinity focal length and mag at MFD. That is assume at a given focal length, that the hiatus remains fixed.

It’s not right, but it’s a better model when focus bracketing than using a thin lens model.

Also, by choosing a sensible overlap CoC and fixed pupil mag, I’ll ensure no ‘focus gaps’

The final realism is that the camera, Canon, isn’t that ‘accurate’ at reporting focus position.

Cheers

Garry

bclaff Forum Pro • Posts: 12,453
Re: Reconciling the Thick Lens Model with P2P Optical Bench

Garry2306 wrote:

...

Bill

Thanks for taking the time to write that.

No problem.

... I’ll pragmatically carry on using the split/thick lens model, based on the manufacturer’s MFD, infinity focal length and mag at MFD. That is assume at a given focal length, that the hiatus remains fixed.

I think you have three cases.

Hiatus unknown. Assume it's zero and computed focal length at MFD using distance and magnification.

Hiatus known at infinity. Still assume zero at MFD and calculate focal length.

Hiatus (and focal length) known at infinity and closer focus.

Then with hiatus and focal length for two or more magnifications you need to choose how to map magnification to hiatus (and focal length?) to get a smooth "reasonable" progression.

All of this is very approximate compared to measured values or Optical Bench when enough is known.

FWIW, the Optical Bench sliders are also approximations based on known lens positions.
Generally it works out quite well.

Regards,

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Bill ( Your trusted source for independent sensor data at PhotonsToPhotos )

Bernard Delley Senior Member • Posts: 1,801
measure the thick lens model parameters
3

internal focus lenses change f and i of the thick lens model with focus setting.

The OB model traces the rays (currently paraxial model?)  from the data of the lens patent. By consequence it knows/tells f and i.

But, you can derive f and i of the thick lens model for "any" finite distance setting of the lens by simple measurements.

measurement get distance object-sensor plane and the LV image gives info on magnification. Repeat  measurement with the same lens settings and a known extension ring to get enough equations for the two unknowns f and i.

The measurement setup would be  improved by having the ruler along the long side of the sensor.

The effective aperture can be determined from the resulting exposure, if a target with fixed radiance is provided. -- For me, the effective aperture is the primary thing to know. The pupil factor is a correct way to deal with (bellows) extension for calculating the effective aperture for an old style lens system with fixed lens positions.  -- The pupil factor is just another parameter that varies with lens setting for internal focus lenses.

 Bernard Delley's gear list:Bernard Delley's gear list
Nikon D7200 Nikon D500 Nikon D850 Nikon AF-S Nikkor 14-24mm f/2.8G ED Nikon AF-S Micro-Nikkor 60mm F2.8G ED +10 more
bclaff Forum Pro • Posts: 12,453
Re: measure the thick lens model parameters

Bernard Delley wrote:

internal focus lenses change f and i of the thick lens model with focus setting.

The OB model traces the rays (currently paraxial model?) from the data of the lens patent. By consequence it knows/tells f and i.

But, you can derive f and i of the thick lens model for "any" finite distance setting of the lens by simple measurements.

measurement get distance object-sensor plane and the LV image gives info on magnification. Repeat measurement with the same lens settings and a known extension ring to get enough equations for the two unknowns f and i.

The measurement setup would be improved by having the ruler along the long side of the sensor.

The effective aperture can be determined from the resulting exposure, if a target with fixed radiance is provided. -- For me, the effective aperture is the primary thing to know. The pupil factor is a correct way to deal with (bellows) extension for calculating the effective aperture for an old style lens system with fixed lens positions. -- The pupil factor is just another parameter that varies with lens setting for internal focus lenses.

I do something like this to determine focal length using a set of extension tubes and a linear fit. These fits are usually quite good.

I find it's very accurate if you use magnification rather than subject distance as subject distance is harder to get very accurately.

With subject distance and an accurate focal length I then estimate the internodal distance but consider that measurement less accurate. Back-fitting into my observed distances has a lot more variation than the focal length fit.

Regards,

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Bill ( Your trusted source for independent sensor data at PhotonsToPhotos )

OP Garry2306 Regular Member • Posts: 108
Re: measure the thick lens model parameters

Bill/Bernard

Thanks for posting your experience.

In fact I’ve been thinking about how evolve my split/thick model.

My current thinking is to use the thick lens model at minimum focus distance at the min and max focal length of a zoom, ie measure mag and calculate the inter nodal at the two focal length extremes.

Then do the same at around the hyperfocal, ie measure the mag, ie around NC/f, but here assume a thin lens model, ie zero inter nodal. 
Then linearly interpolate between focus extremes, ie at x, and the zoom extremes, scaling the inter nodal distance accordingly. 
My logic is that the thin lens is a reasonable model for DoF away from the MFD, but at the MFD a thick lens model is a better model for DoFs.

But I’m still exploring

Bernard Delley Senior Member • Posts: 1,801
just go with the thick lens model
1

Garry2306 wrote:

Bill/Bernard

Thanks for posting your experience.

In fact I’ve been thinking about how evolve my split/thick model.

My current thinking is to use the thick lens model at minimum focus distance at the min and max focal length of a zoom, ie measure mag and calculate the inter nodal at the two focal length extremes.

Then do the same at around the hyperfocal, ie measure the mag, ie around NC/f, but here assume a thin lens model, ie zero inter nodal.
Then linearly interpolate between focus extremes, ie at x, and the zoom extremes, scaling the inter nodal distance accordingly.
My logic is that the thin lens is a reasonable model for DoF away from the MFD, but at the MFD a thick lens model is a better model for DoFs.

But I’m still exploring

I you have two extension rings, you can determine the focal length and the internodal distance also for the infinity setting of the lens.

To check things, I did measurements and least squares analysis for a well documented old lens some time ago: AI 200mm f/4 lens f=199.7mm h=88.7mm

my measurement at infinity setting (f and h are independent of distance setting for this old lens with fixed internal lens positions, but there is a built helicoid extension going with the distance setting) with bellows extensions 50mm 100mm 150mm 200mm gave

Method_1 f= 201.6 RMS= 2.3   h= 89.6 RMS 0.9

Method_2 f= 202.8 RMS= 0.5    h= 84.0 RMS= 2.4

Method_1 agrees within 1 sigma with the known data. Method_1 : eliminating h from the equations and finding f as the mean estimate, then finding the mean of h, is more accurate than doing a linear regression analysis through the data points as Bill mentioned. I think the equi-weighted regression analysis implies a less appropriate error estimate for the measured data compared to Method_1 .

Below is a comparison of  P2P data with my measurement using 0 and 27.5 mm extension ring.

I see two main differences compared to the P2P simulation based on patent data. The camera with this lens reports a less fast lens at 1:1.  The measured internodal distance is quite a bit smaller. However it is plausible by guessing from the eyeballed pupil positions seen from front and back.

 Bernard Delley's gear list:Bernard Delley's gear list
Nikon D7200 Nikon D500 Nikon D850 Nikon AF-S Nikkor 14-24mm f/2.8G ED Nikon AF-S Micro-Nikkor 60mm F2.8G ED +10 more
OP Garry2306 Regular Member • Posts: 108
Re: just go with the thick lens model

Bernard Delley wrote:

Garry2306 wrote:

Bill/Bernard

Thanks for posting your experience.

In fact I’ve been thinking about how evolve my split/thick model.

My current thinking is to use the thick lens model at minimum focus distance at the min and max focal length of a zoom, ie measure mag and calculate the inter nodal at the two focal length extremes.

Then do the same at around the hyperfocal, ie measure the mag, ie around NC/f, but here assume a thin lens model, ie zero inter nodal.
Then linearly interpolate between focus extremes, ie at x, and the zoom extremes, scaling the inter nodal distance accordingly.
My logic is that the thin lens is a reasonable model for DoF away from the MFD, but at the MFD a thick lens model is a better model for DoFs.

But I’m still exploring

I you have two extension rings, you can determine the focal length and the internodal distance also for the infinity setting of the lens.

To check things, I did measurements and least squares analysis for a well documented old lens some time ago: AI 200mm f/4 lens f=199.7mm h=88.7mm

my measurement at infinity setting (f and h are independent of distance setting for this old lens with fixed internal lens positions, but there is a built helicoid extension going with the distance setting) with bellows extensions 50mm 100mm 150mm 200mm gave

Method_1 f= 201.6 RMS= 2.3 h= 89.6 RMS 0.9

Method_2 f= 202.8 RMS= 0.5 h= 84.0 RMS= 2.4

Method_1 agrees within 1 sigma with the known data. Method_1 : eliminating h from the equations and finding f as the mean estimate, then finding the mean of h, is more accurate than doing a linear regression analysis through the data points as Bill mentioned. I think the equi-weighted regression analysis implies a less appropriate error estimate for the measured data compared to Method_1 .

Below is a comparison of P2P data with my measurement using 0 and 27.5 mm extension ring.

I see two main differences compared to the P2P simulation based on patent data. The camera with this lens reports a less fast lens at 1:1. The measured internodal distance is quite a bit smaller. However it is plausible by guessing from the eyeballed pupil positions seen from front and back.

Bernard

I’m keen to try this approach and wondered if you could share the process steps that you undertook. Reading the various posts here has confused me a bit as to how one uses extension rings to work out the inter nodal etc of a lens at, say, the minimum focus distance and ‘infinity’.

Cheers

Garry

Bernard Delley Senior Member • Posts: 1,801
Re: just go with the thick lens model
2

Garry2306 wrote:

I’m keen to try this approach and wondered if you could share the process steps that you undertook. Reading the various posts here has confused me a bit as to how one uses extension rings to work out the inter nodal etc of a lens at, say, the minimum focus distance and ‘infinity’.

You gave the the correct thick lens equation in your opening post. I am slightly elaborating on it. I somehow prefer to use the symbol h instead of your t for the internodal distance. When you turn the focus ring of the lens, you modify the focal length, so f is a function of the 'distance' setting on the lens: f(s) . Also the internodal distance is a function of this setting in general: h(s)

Rewriting, the (your) thick lens equation:

d_i = (2 + 1/m_i + m_i) * f(s) + h(s)

I have also introduced a subscript _i to index the measurements that you do with the same (!) setting of the lens. So each lens measurement yields a pair (triplet) of values:

d_i a sensor - object distance

m_i magnification, derived from the portion of the ruler visible in the image or in LV.

x_i extension ring thickness used, as additional parameter for Method_1

interestingly, the extension ring thickness does not appear in the equation for d_i. But, for each different extension you get another d_i , m_i pair of values. If you have two such measurements, defining 2 equations, you can solve them in Method_1 by realizing the proportionality of m_i with the total extension (ring + internal) of the lens, ex_tot=x_i+e(s):

x_i + e(s) = (1 + m_i)*f(s)

eliminating the unknown internal focus extension e(s) depending on setting s, you find f(s) from

x_1 - x_2 = ( m_1 - m_2 ) *f(s)

In closeup settings of the lens, there may be no extension ring in measurement 2, then x_2=0.

Once you have f(s) , you find h(s) as you already wrote.

If you have several measurements using different extension, then you can find an average f(s) from the different pairs of measurements that can be formed. And you can determine the RMS deviation of each f(s) evaluation from the mean. I would argue the the RMS uncertainty for the mean of f(s) is smaller by a factor sqrt(n-1) than the RMS for the single evaluation. n is the number of measurements. No RMS single can be determined with just two measurements.

I will not go into details of Method_2, which considers a linear regression for d_i and v_i = (2 + 1/m_i + m_i) .

d_i = v_i *f(s) + h(s)

 Bernard Delley's gear list:Bernard Delley's gear list
Nikon D7200 Nikon D500 Nikon D850 Nikon AF-S Nikkor 14-24mm f/2.8G ED Nikon AF-S Micro-Nikkor 60mm F2.8G ED +10 more
OP Garry2306 Regular Member • Posts: 108
Re: just go with the thick lens model

Bernard Delley wrote:

Garry2306 wrote:

I’m keen to try this approach and wondered if you could share the process steps that you undertook. Reading the various posts here has confused me a bit as to how one uses extension rings to work out the inter nodal etc of a lens at, say, the minimum focus distance and ‘infinity’.

You gave the the correct thick lens equation in your opening post. I am slightly elaborating on it. I somehow prefer to use the symbol h instead of your t for the internodal distance. When you turn the focus ring of the lens, you modify the focal length, so f is a function of the 'distance' setting on the lens: f(s) . Also the internodal distance is a function of this setting in general: h(s)

Rewriting, the (your) thick lens equation:

d_i = (2 + 1/m_i + m_i) * f(s) + h(s)

I have also introduced a subscript _i to index the measurements that you do with the same (!) setting of the lens. So each lens measurement yields a pair (triplet) of values:

d_i a sensor - object distance

m_i magnification, derived from the portion of the ruler visible in the image or in LV.

x_i extension ring thickness used, as additional parameter for Method_1

interestingly, the extension ring thickness does not appear in the equation for d_i. But, for each different extension you get another d_i , m_i pair of values. If you have two such measurements, defining 2 equations, you can solve them in Method_1 by realizing the proportionality of m_i with the total extension (ring + internal) of the lens, ex_tot=x_i+e(s):

x_i + e(s) = (1 + m_i)*f(s)

eliminating the unknown internal focus extension e(s) depending on setting s, you find f(s) from

x_1 - x_2 = ( m_1 - m_2 ) *f(s)

In closeup settings of the lens, there may be no extension ring in measurement 2, then x_2=0.

Once you have f(s) , you find h(s) as you already wrote.

If you have several measurements using different extension, then you can find an average f(s) from the different pairs of measurements that can be formed. And you can determine the RMS deviation of each f(s) evaluation from the mean. I would argue the the RMS uncertainty for the mean of f(s) is smaller by a factor sqrt(n-1) than the RMS for the single evaluation. n is the number of measurements. No RMS single can be determined with just two measurements.

I will not go into details of Method_2, which considers a linear regression for d_i and v_i = (2 + 1/m_i + m_i) .

d_i = v_i *f(s) + h(s)

Bernard

Many thanks: very clear.

Now to find some time.

Cheers

Garry

OP Garry2306 Regular Member • Posts: 108
Re: just go with the thick lens model

Garry2306 wrote:

Bernard Delley wrote:

Garry2306 wrote:

I’m keen to try this approach and wondered if you could share the process steps that you undertook. Reading the various posts here has confused me a bit as to how one uses extension rings to work out the inter nodal etc of a lens at, say, the minimum focus distance and ‘infinity’.

You gave the the correct thick lens equation in your opening post. I am slightly elaborating on it. I somehow prefer to use the symbol h instead of your t for the internodal distance. When you turn the focus ring of the lens, you modify the focal length, so f is a function of the 'distance' setting on the lens: f(s) . Also the internodal distance is a function of this setting in general: h(s)

Rewriting, the (your) thick lens equation:

d_i = (2 + 1/m_i + m_i) * f(s) + h(s)

I have also introduced a subscript _i to index the measurements that you do with the same (!) setting of the lens. So each lens measurement yields a pair (triplet) of values:

d_i a sensor - object distance

m_i magnification, derived from the portion of the ruler visible in the image or in LV.

x_i extension ring thickness used, as additional parameter for Method_1

interestingly, the extension ring thickness does not appear in the equation for d_i. But, for each different extension you get another d_i , m_i pair of values. If you have two such measurements, defining 2 equations, you can solve them in Method_1 by realizing the proportionality of m_i with the total extension (ring + internal) of the lens, ex_tot=x_i+e(s):

x_i + e(s) = (1 + m_i)*f(s)

eliminating the unknown internal focus extension e(s) depending on setting s, you find f(s) from

x_1 - x_2 = ( m_1 - m_2 ) *f(s)

In closeup settings of the lens, there may be no extension ring in measurement 2, then x_2=0.

Once you have f(s) , you find h(s) as you already wrote.

If you have several measurements using different extension, then you can find an average f(s) from the different pairs of measurements that can be formed. And you can determine the RMS deviation of each f(s) evaluation from the mean. I would argue the the RMS uncertainty for the mean of f(s) is smaller by a factor sqrt(n-1) than the RMS for the single evaluation. n is the number of measurements. No RMS single can be determined with just two measurements.

I will not go into details of Method_2, which considers a linear regression for d_i and v_i = (2 + 1/m_i + m_i) .

d_i = v_i *f(s) + h(s)

Bernard

Many thanks: very clear.

Now to find some time.

Cheers

Garry

Bernard

I’ve been thinking, which isn’t alway good

My use case is to code in my CHDK Lua script a ‘better’ lens model. Currently I assume a fixed lens thickness, ie that at MFD. This is a conservative view that introduces positive focus lap insurance when focus bracketing, ie the DoF will likely be reduced because of the fixed hiatus. Based on assuming hiatus at MFD is greater than that at infinity.

If I work out the internodal distance, hiatus, using the method you described, it will be right using the focal length you calculate from knowing the two extensions and magnification.  
However, in CHDK and Magic Lantern Lua, the focal length reported is ‘just’ the infinity focal length, ie it doesn’t vary with focus.

I’m therefore thinking that knowing the focal length and thus hiatus at two actual extremes, eg at  MFD and, say, around the hyperfocal, won’t be that useful, if the camera only reports a fixed focal length, ie focal length reporting doesn’t vary with focus. 
I would welcome an6 thoughts you may have, or anyone else. 
Cheers

Garry

bclaff Forum Pro • Posts: 12,453
Math and Measurements of Focal Length etc.

Math of measuring focal length with extension.

Measuring Focal Length
An example with a simple lens

Measuring Focal Length - 50mm f1.8D AF Nikkor

A more sophisticated example including subject distance.

Focal Length at Closest Focus - 105mm f2.8G IF-ED AF-S VR Micro-Nikkor
How to get hyper-accurate magnifications for close-up calculations.

Measuring Magnification

Regards

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Bill ( Your trusted source for independent sensor data at PhotonsToPhotos )

bclaff Forum Pro • Posts: 12,453
Alternative Math using Subject Distance and not Magnification

You can compute focal length as follows

f = sqrt(((s1-s2) * x1 * x2) / (x2 - x1) - 1)

where s is subject to image distance and x is extension.
1 and 2 indicate two different measurements,

Once you have f you can substitute to determine i (hiatus).

I consider this method (far) less accurate than the magnification approach.

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Bill ( Your trusted source for independent sensor data at PhotonsToPhotos )

bclaff Forum Pro • Posts: 12,453
Re: just go with the thick lens model

Bernard Delley wrote:

...

Below is a comparison of P2P data with my measurement using 0 and 27.5 mm extension ring.

I see two main differences compared to the P2P simulation based on patent data. The camera with this lens reports a less fast lens at 1:1. The measured internodal distance is quite a bit smaller. However it is plausible by guessing from the eyeballed pupil positions seen from front and back.

That example is the Nikon AF-S Micro-Nikkor 60mm f/2.8G ED

You stumbled onto a patent where I did not enter all of the pertinent information.
I have now done so and updated the files.
The new files will show a Specified value under NA for 1:2 and 1:1

F# values reported by the Optical Bench are now:

Infinity 2.88 (Scenario 1)
1:4 3.15 (using Focus slider)
1:2 3.55 (Scenario 2)
1:1 4.98 (Scenario 3)

These values are in agreement with the NA values stated in the patent.

Note patent species NA of 0.10 at 1:1 and the Optical Bench now agrees

f# values reported when using the Focus slider are not correct in this situation.

f# and NA current wrong when using Focus slider on this type of patent.

This is a known bug that is on my list of things to fix.

Resoved.

Regards,

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Bill ( Your trusted source for independent sensor data at PhotonsToPhotos )

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