61 replies to this topic

[PrestonE]

Well, Bruce or BRGE and I started this conversation in PM's last 15 June 2024 and today I am going

to start this thread to both help Me and anyone else interested in what it takes to build and test

one of these interferometers.

 

Not sure one would say it is Inexpensive...well not millions of dollars, but likely well beyond what most

of use would be willing to spend on something unless really necessary.

 

Sadly, a BATH interferometer cannot test Fast Concave and Convex surfaces and that is required for

the 2 Corrector lensed in our 18 inch F12 CDK that Mike Jones designed for us.

 

Since One Off Optical Lenses are quite Expensive, like greater than US$5k each we decided to make these

2 lenses at 90mm diameter ourselves.

 

I will give the Lens Radiuses shortly, but first one will need these Abbreviation's to even have a chance of following

this conversation:

 

Thus, the following list to star which may be added to as we go along our way :

 

AI       Adjustable Iris

ASM   Autostigmatic Microscope

BE      Beam Expander with reference behind the BE as to the power ie 2X or 5X ect

CAM1    Camera 120FPS Global Shutter USB Camera

CAM2    Camera Lucid Triton 5.0 MP Model (IMX264)

CCTP   Corner Cube Trihedral Prism

CPF    Circular Polarizing Filter

FM      Folding Mirror

FR       Fresnel Rhomb (Multi-Wavelength 1/2 waveplate Fresnel Rhomb Polarizer Rotator UV/VIS/IR

HWR     Half wave retarder alternate name for HWP

HSPMI    High Stability Plane Mirror Interferometer i.e. the Zygo 7006A

MgF2   MgF2 Window

MO      Microscope Objective

MUT    Mirror undertest is in the test arm at a distance equal to its RoC from the point where the MO brings the test beam to a focus.

MWPR  Multi Wavelength Polarizer Rotator

NDF     Neutral Density Filter

NPBS   Non Polarized Beam Splitter

OPD    Optical Path Difference

OPL     Optical Path Length

PBS     Polarized Beam Splitter

PSI      Phase Shift Interferometer

PH       Pin Hole

QWP   Quarter Wave Plate

QWR    Quater Wave Retarder alternate more descriptive name for a QWP

SNB     Silicon Nitride Ceramic Ball

TG       Tywman Green Zygo 7006

TG LUPI   TG interferometer with unequal path length for test and reference beams  (requires long coherence  length monochromatic light source)

 

With Bruce's Very Kind help in telling us what we need to purchase, we hope that we have purchased everything

needed for the construction and can now move forward.

 

We have machined various holders for Lenses, Filters, ect and will likely be machining more parts required as we go.

 

We have also 3D Printed various parts and stands to test thing and concepts that may need to be machined in aluminum

or SS as we go along

 

Hopefully, this will be interesting and beneficial so some of you.

 

Very Best Regards,

 

Preston

Edited by PrestonE, 14 March 2025 - 03:44 PM.

[Oregon-raybender]

Looking forward to the seeing the project. I was glad to help

make some of Tinsley's  units, way back in the day, 1970's

We used good microscope lenses, then built their own.

 

Take lots of images and offer drawings and notes on your progress.

 

Good Luck.

 

Starry Nights

[duck]

Really interesting project.  That CAM1 might be like the camera I have on my Fizeau.  I didn't know what I was buying at the time.  USB and board level for ease of mounting were my tipping points.  That it has a global shutter is really paramount, but I didn't know it at the time.

[BGRE]

Actually CAM2 is more critical as its polarisation sensitive and has a global shutter.

[PrestonE]

I have to really thank BGRE Bruce, as you guys can not see our 18 pages of over 20 PM's per page!!!

 

I have read and reread them all dozens of times, and learn something each and every time.

 

However, this is above my pay grade and rather than hash it out in private we decided that it would

hopefully benefit the community to do this together.

 

My understanding of all of this is rather limited, so I really look forward to adding to the details tomorrow

with pictures and diagrams of what I hopefully understand tomorrow and what I do not will hopefully be

discussed in enough detail to at least get this Interferometer working...even if I never totally understand

exactly what I am doing.

 

Will include many of those from our PM's over the past almost year of discussions.

 

MKV Mladen and Gleb1964 were also involved in these PM's and my thanks goes out to them also.

 

Chat more tomorrow,

 

Preston

[BGRE]

The interferometer is essentially a Twyman-Green spherical wave LUPI that uses polarisation optics and a polarisation sensitive camera to implement instantaneous PSI.

To avoid the high cost of a long coherence length single frequency laser source a means of adjusting the OPD piston term is used to allow use of a multimode HeNe laser with adequate fringe contrast.

Adjustment of the relative power of the test and reference beams is also possible to maximise fringe contrast for a wide range of test surface reflectivity. In principle even AR coated surfaces could be measured.

 

A separate alignment camera is used as using the polarisation sensitive camera for this is far from ideal.

Instantaneous PSI mitigates the effects of turbulence in the measurement cavity as well the effects of vibration through averaging (not of interferograms but of wavefronts).

 

To minimise retrace errors defocus and tilt fringes should be avoided complicating correct wavefront averaging for non instantaneous PSI.

If you are averaging hundreds of wavefronts with small residuals that may have features that change between hill and hollow from wavefront to wavefront due to noise, vibration and turbulence techniques such as using a thumb to raise a thermal bump on the test surface so that the true sign of wavefront residuals can be determined are of zero value.

 

Since the interferometer components aren't perfect, the interferometer will have residual errors which need to be measured.

Similarly, there will also be residual phase shift errors which will be unique to each pixel, so a means of measuring these will also be required.

 

The challenge is minimising the total cost of the interferometer components whilst achieving acceptable performance.

Edited by BGRE, 14 March 2025 - 12:53 AM.

[duck]

Looking forward to the education.  And also Preston's most likely beautiful execution.

[PrestonE]

Duck, you are very Kind...though I am certain that my execution will not be up to
what most that know me would call Beautiful.

One of the main reasons that I am doing this is that I am Lost Much of the time
and we thought if I tried to Explain it to others...just perhaps something would
click in my 70 year old brain.

 

Best Regards,

 

Preston

[PrestonE]

We think that this should be done in sections to get me more up to speed and try to keep
from totally jumping around and confusing anyone more than me.

 

Thus, I propose we do the following so everyone understands what and why certain things
were purchased for this build.

 

I will be going from PM's from Bruce and others during this discussion...as I have already said
that I Do NOT Fully understand this At ALL at this point.

 

I ask you all to jump in and correct me when I say something that is Incorrect, Please!!!  as I
know that there are several here Far More Knowledgeable than me on this subject.

 

Sections will be as follows and we may add some as needed:

 

1) Laser

 

2) Polarization Rotator - Fresnel Broadband halfwave retarder

 

3) OPD adjuster/Variable optical delay line - uses Zygo HSPMI

 

4) Beam Expanders

 

5) Random Ball Calibrator

 

6) Alignment Camera

 

7) Imaging Camera

 

I would love to just start posting pictures of where we are currently at, but really think that
would be of more harm than good at this point...hopefully within a week once we cover some of these
basics.

 

Very Best Regards,

 

Preston

[PrestonE]

Corrector Lens Radiuses are as follows and are about 85mm or 3.3" Outside Diameter:

 

Element 1   11.391" CC              

                     8.589" CX

 

                    This is the easier one.

 

Element 2      6.818"CX
                      5.215"CC

 

                      This one has a curve under F1

 

These curves will be modified as each curve is finished and those
measurements are recalculated to Best Fit.  I have left out the
prescription including thicknesses per a request and for this discussion
they really are not necessary.

 

Some will say why not just do Contact IF between the Test Plate and the final curve,
but at these steep curves it is Very Difficult to Define the Quality of
the Curve without something like this Twyman-Green Interferometer that we
will construct. 

 

Additionally, we will be making some 330mm Diameter lenses in the future for Ed Jone's ACS scope

with Convex Surfaces and do not want to have to make Test Plate to Test these...and this instrument

will be able to Test those surfaces directly.

 

So as not to ramble on or mix things up too much, we will live this here and
start the "Laser Section" next.

 

Regards,

 

Preston

Edited by PrestonE, 14 March 2025 - 03:25 PM.

[duck]

this IF is able to test convex surfaces directly?

[PrestonE]

If I understand correctly, but hopefully Bruce can confirm?

 

We have Test Balls of Silicon Nitride 1 inch in diameter for Calibration,

and thus if those are used and are Convex that would be my understanding.

 

But, as I stated before...this is All Above My Pay Grade!!!

 

Preston

[BGRE]

With the aid of an auxiliary lens (or equivalent optical system) that converts the divergent spherical wave output to a convergent beam that fully illuminates the convex test surface at normal incidence. This is the approach used by Difrotec in their D7 PDI. Otherwise, the interferometer can be used to test the testplates.

 

Depending on the lens prescriptions the number of testplates required may be able to be drastically reduced by testing its surfaces against the testplate using a wide airgap rather than one of a few microns.

[BGRE]

If I understand correctly, but hopefully Bruce can confirm?

 

We have Test Balls of Silicon Nitride 1 inch in diameter for Calibration,

and thus if those are used and are Convex that would be my understanding.

 

But, as I stated before...this is All Above My Pay Grade!!!

 

Preston

The range of RoC for convex surfaces that can be directly measured is limited by the microscope objective working distance.

The microscope objective NA should be somewhat greater than that of the test surface. In practice for suitable readily available microscope objectives the maximum measurable convex surface RoC < 34mm depending on the exact microscope objective used.

For convex surfaces with larger RoCs a "microscope objective" with a built in beam expander is required. This can be implemented with a standard infinity corrected microscope objective and an auxiliary lens. The auxiliary lens diameter has to be larger than that of the test surface and its working distance larger than the test surface RoC.

Since the interferometer is used on axis with zero tilt or defocus fringes the field aberrations of this auxiliary lens are relatively non-critical. If the output beam is faster than F/8 or so the RBT can be used to measure the wavefront errors produced by this auxiliary lens. 

[BGRE]

A single concave "testplate" with an RoC of around 9" and a diameter of around 4.5" could be used to measure both convex surfaces of the 3.3" diameter lenses in an on-axis Fizeau instantaneous PSI setup by reconfiguring the interferometer and using a quarter wave retarder plus a short coherence length 635nm source such as a 635nm multimode diode laser source.

 

Another option is to test the convex surfaces through the concave surface with a Twyman-Green setup (after the concave surface is finished). However, a short coherence length source will be required along with adjusting the OPD piston term to within a few microns of zero for reflections from the convex surface. Raytracing will be required to check if the resultant aberrations are acceptably small.

[PrestonE]

Laser Selection:

 

Bruce recommended a Linearly Polarized  HeNe  Laser for this project.  His discussion with me
went through why we could not use the Diode Type lasers that were used in our BATH, but
that conversation in our PM's is no longer available. 

 

Thus, if anyone has question regarding exactly why we need a Linearly Polarized Laser
I will defer to Bruce explaining once again.

 

In attempting to find one on EBay, we ended up purchasing a Melles Griot 05-LHR-321-61
based on information from Sam's Laser Pages.  This however was misinterpreted and was
a Randomly Polarized Laser...and the power supply did not cause the laser to start
upon receipt.

 

Thus, it was back to the drawing board to finally find a Melles Groit 05-LHP-121 2mW laser.

(actual power 3.4-4.7mW) 632.8 nm, polarization 500:1, Beam Diameter 0.59mm, 

 

And the calculation of Exposure times with this 2mW laser and all of the downstream components
done by Bruce:

 

ESTIMATION of Exposure time:

 

1) Laser power output 2mW

2) Beam expander throughput 90% (likely a little higher)

3) CPL based polarization rotator throughput ~70%

4) HSPMI throughput ~80%

Resultant power at HSPMI output ~ 1.0mW

5) Beam expander throughput ~90%

6) Twyman-Green beam splitter throughput to test beam ~40%

7) CPL one way throughput ~80%

8) Overfill loss ~50%

9) Test surface reflectivity ~ 4%

10) CPL transmission ~80%

11) Beam splitter throughput to camera arm ~40%

12) Resultant camera arm return test beam power ~ 1.8uW

13) linear polarizer transmission ~40%

14) Camera lens transmission ~80%

15) Power incident on image sensor ~580nW

16) Image sensor quantum efficiency ~50% @633nm

17) Photon energy @633nm ~3.3E-19J

18) Photon flux at image sensor ~ 1.8E12 photon/sec

12) Test surface image diameter 4000 pixels

13) Pixel signal ~7115 photoelectrons/sec

14) Pixel well depth ~10,000 electrons

15) Exposure time for full pixel at fringe peak ~70 milliseconds

 

Thus some work on improving efficiency is required.

 

By optimizing the orientation of the plane of polarization at the HSPMI input and using
a high reflectance reference mirror in the Twyman-Green reduces the exposure time by a
factor of 5, Using a halfwave retarder based polarization rotator reduces the exposure time by a factor of 2.
Reducing the test surface image diameter by a factor of 0.7 gains reduces the exposure time by a factor of 2.

 

Substituting a PBS + 3 QWPs for the NPBS + 2 CPLs reduces the exposure time by a factor of at least 5.
At this point substituting a monochrome image sensor with a global shutter would achieve another factor of
2 reduction in exposure time.

 

If all the above measures were implemented an exposure time of around a couple of hundred microsec could be
achieved. A back illuminated image sensor would increase the quantum efficiency by up to 2x.

 

Thus a 2mW laser output is the best compromise between power output and a small number of longitudinal lasing
modes coupled with relatively small fluctuations of laser output during mode sweeping.

 

Regards,

 

Preston

 

ps, one can see why it is easy to quickly end up in the weeds as far as following this discussion!

Edited by PrestonE, 15 March 2025 - 04:00 PM.

[Arjan]

"With the aid of an auxiliary lens (or equivalent optical system) that converts the divergent spherical wave output to a convergent beam that fully illuminates the convex test surface at normal incidence."

For a 330 mm diameter convex test surface, wouldn't that require very large diameter auxiliary lens? What quality does it need to have?

[BGRE]

Yes, an auxiliary lens with a clear aperture at least equal to that of the test surface would be required.

The residual wavefront error contribution of this lens would need to be a small fraction of a wave but not as small as 1/100 wave or less as the residual errors of the interferometer and auxiliary lens can be calibrated. For fast convex surfaces either a multielement lens or aspherisation of one surface of a single element auxiliary lens would be required. In most cases the relaxed performance specs of a Fizeau illumination system with a relatively small Fizeau cavity and a concave testplate is more practical. However, implementing instantaneous PSI with a Fizeau is a little more challenging but neither impossible nor even prohibitively expensive. If feasible using the lens under test as part of the illumination system avoids the expense of a large lens and the requirement for a reference element with an aplanatic rear surface. The design complexity would be somewhat akin to that of a transmission sphere with a large concave reference surface when viewing the cavity through the rear of the reference element with some relaxation of residuals due to a relatively short cavity.

 

Conventional testplating without an illumination system that ensures approximately normal illumination of the test and reference surfaces is problematic with fast test surfaces in that the effective wavelength varies across the test surface complicating correct fringe interpretation.

You also need a very large area illumination source and a large beamsplitter plate when testing a convex test surface through the back of the testplate. 

An individual testplate is required for each test surface with a different RoC.

The expense of 4 large diameter testplates/reference surfaces can often be reduced by using a larger airgap with better illumination optics so that a reference surface can be shared by more than one test surface.   

Edited by BGRE, 15 March 2025 - 04:20 PM.

[BGRE]

Randomly polarised HeNe lasers are only random insofar that the plane of polarisation is randomy oriented with respect to the laser tube and for a fraction of these this orientation is stable. Short cavity randomly polarised HeNe lasers oscillate in a pair of orthogonal linear polarised modes one of which can be selected with a suitably oriented linear polariser. A fraction of those lasers with a stable plane of polarisation orientation will have a stable output power for each mode particularly after the laser fully warms up. One mode may even have significantly more power than the other. If one has a sufficient number of lasers to choose from then like Zygo selection of suitable short cavity "randomly" polarised laser with stable orientation of the plane of polarisation with one mode dominant could be used as a relatively inexpensive long coherence length (> 100m) source. However, the yields are unknown and the supply of such lasers may have been cherry picked. 

 

To avoid the potential cost with the somewhat uncertain yield of such a selection process a method of using a multimode linearly polarised laser to achieve high fringe contrast for any OPD was chosen.

Using a laser with a known resonator cavity length of a few cm that only oscillates in a small number of modes reduces the required OPD  adjustment accuracy. Using a 633nm HeNe laser allows advantage to be taken of the availability of polarisation components in the form of distance measuring interferometer components from scrapped wafer steppers etc. Sometimes unused components that were stocked as spares are available as newer distance measuring interferometers use monolithic interferometer assemblies.

Often a subassembly comprising a PBS, a corner cube and a couple of QWP can be obtained for a small fraction of the price of a single new QWP with the same (~20mm) clear aperture.

[BGRE]

 

The above diagram illustrates the drop in fringe contrast for a multimode laser when the OPD approaches an odd multiple of the laser cavity length.

Fringe contrast is maximum whenever the OPD is close to an even multiple of the laser cavity length. Since the coherence length of an individual mode of most common short cavity HeNe lasers exceeds 100m after the laser has warmed up a simple adjustment of the OPD piston term can be used to optimise the fringe contrast. Maximising fringe contrast is also important for a phase shift interferometer with not tilt, defocus or SA fringes.

Adjustment of the OPD piston can either be done in the source or with a Twyman-Green by adjusting the reference arm OPL. For a Fizeau only the former option is practical and usually a very short coherence length source is required along with a precise tuning of the OPD to near zero.

 

[Kitfox]

It's not that there are more or better DSOs in the southern sky.  (Though there are some awesome ones!)  It is that anything that appears in the southern sky for such a brief time.  Their visibility is a result of how the sky moves.

 

Objects in the southern sky are only above the horizon for two or three months at a time, and much of that is at low elevations.  Objects that appear in the eastern or western sky are above the horizon for eight or nine months of the year.  And objects in the north are above the horizon all year long.

 

300 feet is within the reach of cat 5 Ethernet cable.  If you can reduce the distance a little bit, you would have an excellent signal through cable.  I ran for years with 250 feet of buried cat 5 cable.  I ran remotely all that time with no problems at all.

 

I have used a few types of IF units in the past (darn, 40 years ago now), but I feel like I’m getting lost fast now that I’m getting “into the weeds” as Preston stated so well.  I stole this image off the ‘net (Creator: Zecchino, Michael ©):

 

 

If this is where we are going, someone please describe the parts; if not, what are the differences?  I apologize for the limited knowledge (read: ignorance), but I truly want to learn this process 

[BGRE]

It's somewhat like that but with the addition of OPD piston adjustment (to maximise fringe contrast) and instantaneous PSI using polarisation techniques to manipulate the Pancharatnam/Berry Geometric phase. This avoids wavefront inversion issues between exposures and is immune to vibration and turbulence effects. To minimise retrace errors no tilt or defocus between test and reference return beams is used.

Calibration of interferometer residual wavefront errors and the residual phase shift errors of the geometric phase shifter has also been added.

 

Strictly the diverger optics are an integral part of the imaging optics that image the test surface onto the camera image sensor. 

 

Adjusting the ratio of the return test and reference beam powers is also required to optimise fringe contrast. 

A halfwave retarder is used to clock the plane of polarisation of the source to do this. The test and reference incident beams are orthogonally linearly polarised so that clocking the source plane of polarisation can be used to maximise the fringe contrast.

For those who wondered why maximising fringe contrast matters if there are no fringes, the modulation of the camera image brightness as the phase shift between the test and reference return beams is changed by the phase shifter is maximised when the conditions for maximum fringe contrast are met.

 

For a discussion of various geometric phase shifters see: 

https://wp.optics.ar...se_Shifter.pdf 

 

N.B. The paper appears to use Mathematica or a similar symbolic maths package.

[Arjan]

"Yes, an auxiliary lens with a clear aperture at least equal to that of the test surface would be required.

The residual wavefront error contribution of this lens would need to be a small fraction of a wave but not as small as 1/100 wave or less as the residual errors of the interferometer and auxiliary lens can be calibrated"

Okay. Shouldn't such a lens be added to the 7 sections Preston proposed, as it will be required for testing convex surfaces and will be a significant cost driver?

[BGRE]

No, because the original idea was to use testplates for the convex surfaces as its considerably cheaper than a fast largish diameter auxiliary lens, even if a short cavity (~3" for the 3.3 inch diameter lenses) Fizeau IF has to be used to minimise the number of testplates required.  With a short 3" cavity the maximmum illumination optics angular error is a generous 50 arcsec.

 

The lowest cost approach for the 3.3" meniscus lenses is to figure the concave side first using the spherical wave Twyman-Greem to measure the surface errors. Then polish the convex surface and test against a concave reference surface (tested using the Twyman-Green) viewing the Fizeau cavity through the concave surface. Raytracing can be used to determine the maximum usable airgap for this configuration. With some ingenuity phase shifting should be possible as long as the test and reference beams OPL's are closely matched.

 

For the larger double biconvex lenses it may be possible to use a single (or at least fewer than 4) concave reference surface.

It should be feasible to illuminate the resultant Fizeau cavities through the biconvex lenses.

If the Fizeau cavities are viewed through the back of the reference spheres then the illumination optics become akin in complexity to those used in Fizeau concave transmission spheres.

Edited by BGRE, 16 March 2025 - 07:27 AM.

[PrestonE]

On to the next section:

 

2) Polarization Rotator - Fresnel Broadband halfwave retarder

 

This is the reply from Claude 3.5 to the below question regarding how it works with a Linearly Polarized Laser Beam.

 

From looking at my conversations with Bruce this seems to align well and is clearer than I could ever possible try

to put into words...if there are errors, I am sure Bruce will say so.

 

Question to Claude 3.5

 

"Physics of what happens to a Linearly Polarized Laser beam passing through a Fresnal Rhomb Polarizing 1/2 wave

retarder when the wave plate is rotated."

 

Reply from Claude,

 
When a linearly polarized laser beam passes through a Fresnel rhomb configured as a half-wave retarder (λ/2),

the following physics occurs as the retarder is rotated:

 

1) Basic function:

 

A half-wave retarder introduces a 180° (π) phase shift between the two orthogonal polarization components
This flips the polarization direction across the fast axis of the retarder.

 

2) Rotation effects: 

 

When the half-wave retarder is rotated by angle θ, the output linear polarization rotates by 2θ
If the input polarization is at angle φ, the output polarization will be at angle (2θ-φ)
This is described mathematically by the Jones matrix for a half-wave plate.

 

3) Fresnel rhomb specifics:

 

 

Unlike thin crystal waveplates, Fresnel rhombs achieve retardation through total internal reflection
They're less wavelength-dependent than crystal waveplates
A standard Fresnel rhomb is typically a quarter-wave retarder, so to create a half-wave retarder,

two rhombs are often used in series.

 

4) Conservation principles:

 

Total intensity remains constant during rotation (assuming no absorption)
The beam remains linearly polarized at all rotation angles
Only the orientation of the polarization plane changes.

 

5)Observable effects:

 

If analyzed with a polarizer after the rhomb, the transmitted intensity will vary as cos²(2θ-φ-α), where α is the polarizer angle
This creates a complete extinction/transmission cycle twice per 360° rotation of the rhomb

This rotation property makes half-wave retarders valuable in optical systems for precisely controlling polarization orientation

without changing other beam properties.

 

Best Regards,

 

Preston

Edited by PrestonE, 16 March 2025 - 09:43 AM.