Eric Lerner is presenting his recent paper on a static universe on PhysicsForums

[SelfSim]

To resolve the issue (pardon the pun) I've sent an E-mail to NASA via the Galex HelpDesk (yes it does exist) if they can provide actual performance data on the angular resolution.

Awesome!

I hope they produce it before the thread gets locked (as per the threat by the mods to do so ... albeit for totally unrelated reasons).

From his response (post#71), it seems he's standing by his methodology which appears to take the "assume we don't know how it works .. and just go with what's in front of us" approach .. (rather than a theoretical scope design oriented one). I don't think this is a particularly sound approach with any dataset, and relying on his produced stellarity distributions as the criteria, seems to lack in the 'checks and balances' department .. (IMHO) ..

I'm prepared to yield if he can show why he's right .. at the moment all we have is (a sort of) "believe in us .. and our methodology" justification.

I've noticed Lerner is becoming increasingly defensive with other posters and may no longer respond.
Let's wait until the info (hopefully) comes from NASA.
If ultimately he believes he is wrong then he should retract the paper from the Monthly Review of the Royal Astronomical Society.................... and the reviewers be reviewed.

I doubt we'll end up with him agreeing to do that .. but I hope we'll find out ...
Cheers

 

[sjastro]

Awesome!

I hope they produce it before the thread gets locked (as per the threat by the mods to do so ... albeit for totally unrelated reasons).

From his response (post#71), it seems he's standing by his methodology which appears to take the "assume we don't know how it works .. and just go with what's in front of us" approach .. (rather than a theoretical scope design oriented one). I don't think this is a particularly sound approach with any dataset, and relying on his produced stellarity distributions as the criteria, seems to lack in the 'checks and balances' department .. (IMHO) ..

I'm prepared to yield if he can show why he's right .. at the moment all we have is (a sort of) "believe in us .. and our methodology" justification.

I doubt we'll end up with him agreeing to do that .. but I hope we'll find out ...
Cheers

On p. 684 of this reference it gives the resolution (FWHM) of the GALEX telescope as 4.2 arcsec in FUV and 5.3 arcsec in NUV. As explained in our 2014 paper, we based the actual resolution on what was the minimum radius galaxy that the telescope, plus the algorithms used to account for the PSF, classified as an extended source. This could be done unambiguously because the stellarity distribution produced by these algorithms (the ones in the GALEX and HUDF catalogs respectively) had two clear peaks for point sources and extended ones. So setting the threshold anywhere near where we did at 0.4 produces the same results. Unsurprisingly this measure of radius resolution turns out to be half the FWHM resolution. In the 2014 paper we also consider the effect on our conclusions of the uncertainty in the determination of the resolutions. As you point out, the GALEX designers picked the focal length to produce a wide field of view, which also limited the resolution to a much larger value (poorer resolution) than was optically possible. You can't optimize a single telescope for everything. For HUDF, we checked the actual resolution in each filter by the same method and did not see a significant variation. This is what the data showed, so this is what we went with. We do note that at z=5 a large fraction of the galaxies are not resolved. The median is not a good estimate of population mean once most of the galaxies in the redshift bin are not resolved, so HST measurements much beyond z=5 are not going to be highly reliable.

The FWHM values quoted seem to be based on the procedures described in 5. RESOLUTION pg 691.
As described in the procedure bright stars are used that lead to saturated cores in the PSF (point spread function).
Saturation or near saturation leads to high FWHM values; the procedure is performed to show details in the wings.
In reality if the FWHM values are an indication of angular resolution performance then the telescope has poor optics, is slightly out of focus or is seeing limited due to the atmosphere.
The latter is obviously not applicable to Galex.

If we play the devil’s advocate and assume the FWHM values do indicate performance then Lerner’s method is still wrong as any value less than the FHWM is a point source and beyond measurement yet Lerner’s cut off is around 50% of the FWHM values for the FUV and NUV bands.
Hopefully NASA will provide us with the performance data.

It doesn’t need reminding but the dependence of wavelength on resolution is illustrated on the Hubble site.

Here we will try to answer the related question of how close together two features can be and still be discerned as separate – this is called the angular resolution.

The Rayleigh criterion gives the maximum (diffraction-limited) resolution, R, and is approximated for a telescope as
R = λ/D, where R is the angular resolution in radians and λ is the wavelength in metres. The telescope diameter, D, is also in metres.

In more convenient units we can write this as:
R (in arcseconds) = 0.21 λ/D, where λ is now the wavelength in micrometres and D is the size of the telescope in metres.

So for Hubble this is:
R = 0.21 ｘ 0.500/2.4 = 0.043 arcseconds (for optical wavelengths, 500 nm) or
R = 0.21 ｘ0.300/2.4 = 0.026 arcseconds (for ultraviolet light, 300 nm).

Note that the resolution gets better at shorter wavelengths, so we will use the second of these numbers from now on.

It emphasises that Lerner cannot ignore wavelength.

 

[sjastro]

Galex performance.

The design yields a field-averaged spot size of 1.6 arcsec (80%EE) for the FUV imagery and 2.5 arcsec (80%EE) for the FUV spectroscopy at 1600A. NUV performance is similar. There is no in-flight refocus capability.

While the 1.6 arcsec result is much higher than the theoretical diffraction limited performance it is nowhere near the FWHM values quoted by Lerner as being indicative of actual performance.

GR1 Mission & Instrument Overview

 

[SelfSim]

Galex performance.
...
While the 1.6 arcsec result is much higher than the theoretical diffraction limited performance it is nowhere near the FWHM values quoted by Lerner as being indicative of actual performance.

GR1 Mission & Instrument Overview

Does "the design yields a field averaged spot size" mean that the scope has been tested and then returns that performance figure? (Haven't read the link yet .. will do shortly ..)
Huge difference from 4.2 arcsecs FWHM!!!

 

[SelfSim]

Huge difference from 4.2 arcsecs FWHM!!!

And with that comment I've stumbled into yet another unclear domain raised by Lerner's first (UV surface Brightness) paper:
Was his model sufficiently detailed as to compensate for the different ways of citing optical performance across the HUDT and Galex scopes (ie: FWHM vs Encircled Energy (EE)) when coming up with his 1/38 ratio, (θmGALEX/θmHUDF)?
If so, what impact does this have on his conclusion?

 

[sjastro]

Does "the design yields a field averaged spot size" mean that the scope has been tested and then returns that performance figure? (Haven't read the link yet .. will do shortly ..)
Huge difference from 4.2 arcsecs FWHM!!!

The scope was tested by measuring the pixel radius and profile of various stars from CCD images from which the 80% ensquared energy is determined.
The spot size is then calculated.
I have been trying to find Galex images which haven't been over processed, colourized and have a high signal/noise ratio so I can use my own astroimaging software to calculate the spot sizes.

The FWHM figures quoted in the table refer to the spatial resolution of the telescope/camera set up and shouldn't be confused with the performance value.
I also noticed they seem to vary according to the reference document.
In this one it is 4.0 arcsec in FUV and 5.6 in NUV.
In others it is 4.2 arcsec in FUV and 5.3 in NUV.

 

[sjastro]

And with that comment I've stumbled into yet another unclear domain raised by Lerner's first (UV surface Brightness) paper:
Was his model sufficiently detailed as to compensate for the different ways of citing optical performance across the HUDT and Galex scopes (ie: FWHM vs Encircled Energy (EE)) when coming up with his 1/38 ratio, (θmGALEX/θmHUDF)?
If so, what impact does this have on his conclusion?

In a nutshell he hasn't considered anything.
Frankly the Galex data is a side issue, what kills off Lerner's model stone dead is the Hubble data.
The Hubble/ACS/WFC produces images that are oversampled compared to Galex and therefore operate closer to the theoretical limit for resolution which show up the differences in resolution for the filters which Lerner's cutoff procedure does not.

Lerner's model can be simply rejected because the cutoff process doesn't work.

 

[SelfSim]

In a nutshell he hasn't considered anything.
Frankly the Galex data is a side issue, what kills off Lerner's model stone dead is the Hubble data.
The Hubble/ACS/WFC produces images that are oversampled compared to Galex and therefore operate closer to the theoretical limit for resolution which show up the differences in resolution for the filters which Lerner's cutoff procedure does not.

Lerner's model can be simply rejected because the cutoff process doesn't work.

So I'm still not quite sure I understand that fully yet(?)
You pointed out in in post #22:

If we play the devil’s advocate and assume the FWHM values do indicate performance then Lerner’s method is still wrong as any value less than the FHWM is a point source and beyond measurement yet Lerner’s cut off is around 50% of the FWHM values for the FUV and NUV bands.

Does this ~50% come from his choice of applying the 1/38 ratio across both bands (which includes HUDT data which is clearly subject to the filter/resolution issue)?

 

[sjastro]

So I'm still not quite sure I understand that fully yet(?)
You pointed out in in post #22:
Does this ~50% come from his choice of applying the 1/38 ratio across both bands (which includes HUDT data which is clearly subject to the filter/resolution issue)?

For the Galex data since Lerner claims the FWHM values of 4.2 arcsec in FUV and 5.3 in NUV represent resolution limits then his cut off values should reflect the same values.
Instead they are 2.4 and 2.6 arcseconds respectively which are around 50% lower.
His cut off values for the Hubble data are just as meaningless for different reasons as they are same irrespective of the filter used.
The 1/38 ratio might as well be a random number as his cut off values do not make any sense.

The quoted FWHM values for Galex has only served to cloud the issue somewhat, the Hubble data provides a more straightforward of refutation of Lerner's methodology by its failure in finding resolution differences in the individual filter data.

 

[SelfSim]

For the Galex data since Lerner claims the FWHM values of 4.2 arcsec in FUV and 5.3 in NUV represent resolution limits then his cut off values should reflect the same values.
Instead they are 2.4 and 2.6 arcseconds respectively which are around 50% lower.
His cut off values for the Hubble data are just as meaningless for different reasons as they are same irrespective of the filter used.
The 1/38 ratio might as well be a random number as his cut off values do not make any sense.

The quoted FWHM values for Galex has only served to cloud the issue somewhat, the Hubble data provides a more straightforward of refutation of Lerner's methodology by its failure in finding resolution differences in the individual filter data.

Thanks for that .. much clearer now, and a very elegant refutation I might add!

Many thanks for your clarity on this atypically uninterrupted thread.. and all credits to you for helping us in understanding a quite technical issue. (And all in only 2 pages! )

Cheers

 

[sjastro]

Thanks for that .. much clearer now, and a very elegant refutation I might add!

Many thanks for your clarity on this atypically uninterrupted thread.. and all credits to you for helping us in understanding a quite technical issue. (And all in only 2 pages! )

Cheers

Thanks.
While both of us can spot the flaws in the outcomes of Lerner's methodology neither of us are in a position of knowing how the outcomes came about in the first place.
Now that Jean Tate has come into the thread with a focus on the procedural aspects, hopefully we might gain an insight should Lerner decide to respond.

 

[SelfSim]

It seems that Eric still isn't seeing eye-eye with us about the optical resolution/wavelength issue.

He's basically confirmed that his method deliberately uses the spatial resolution parameter of the telescope/camera combo (rather than the scope optical performance/wavelength performance). Seems to me that pixel size and oversampling still can't compensate for the impacts introduced by filtering in the optical pathway?

 

[sjastro]

It seems that Eric still isn't seeing eye-eye with us about the optical resolution/wavelength issue.

He's basically confirmed that his method deliberately uses the spatial resolution parameter of the telescope/camera combo (rather than the scope optical performance/wavelength performance). Seems to me that pixel size and oversampling still can't compensate for the impacts introduced by filtering in the optical pathway?

On GALEX, measurement, etc. Selfsim—you did not read my comment that my measured resolution refers to radius while FWHM refers to diameter. The key point is that with both Hubble and GALEX the resolution is mainly linked to the pixel size. That is why it is not linked to the wavelength—the pixel size does not change with wavelength.

Lerner doesn’t seem to realise it’s the number of pixels the photons fall on which is the important parameter.
If the resolution is decreased by filter choice, bad seeing, poor optics etc, then more light falls onto adjacent pixels which affect the radius or diameter of the FHWM or ensquared energy value.

I’ve decided to put the resolution vs filter saga to the test by downloading some f435w and f814w filtered data for the object Messier 30 from the Hubble legacy archive site.
The ACS was used but unlike the HUDF images an 814W filter was used instead of the 850LP.

Unlike previous discussions where only the optics were considered, the system angular resolution which links both wavelength and pixel size is defined by the equation.

System angular resolution ≈ [(0.21λ/2.4)² + (0.05²)]º̇⁵

The 0.05 term is the size of the ACS pixels in arcsec.
For a 435W filter the theoretical resolution is 0.062 arcsec and the 814W filter is 0.087 arcsec.

For the Messier 30 data, the same six stars of medium brightness were handpicked for each filter so as not to distort the FWHM measurements.
AIP4WIN software was used for the measurements.
In all cases the FWHM of the stars were higher in the 814W data, the results being:

435W data FWHM = 0.279 +/- 0.035
814W data FWHM = 0.326 +/- 0.058

By comparison my puny telescope at sea level has an average FWHM value around 10X higher than Hubble.
A larger sample size would be preferable but the dependence of resolution on wavelength is apparent.

Irrespective of what method Lerner employs the lack of differentiation of resolution between the Hubble filtered data is telling.

 

[SelfSim]

Lerner doesn’t seem to realise it’s the number of pixels the photons fall on which is the important parameter.
If the resolution is decreased by filter choice, bad seeing, poor optics etc, then more light falls onto adjacent pixels which affect the radius or diameter of the FHWM or ensquared energy value.

I’ve decided to put the resolution vs filter saga to the test by downloading some f435w and f814w filtered data for the object Messier 30 from the Hubble legacy archive site.
The ACS was used but unlike the HUDF images an 814W filter was used instead of the 850LP.

Unlike previous discussions where only the optics were considered, the system angular resolution which links both wavelength and pixel size is defined by the equation.

System angular resolution ≈ [(0.21λ/2.4)² + (0.05²)]º̇⁵

The 0.05 term is the size of the ACS pixels in arcsec.
For a 435W filter the theoretical resolution is 0.062 arcsec and the 814W filter is 0.087 arcsec.

For the Messier 30 data, the same six stars of medium brightness were handpicked for each filter so as not to distort the FWHM measurements.
AIP4WIN software was used for the measurements.
In all cases the FWHM of the stars were higher in the 814W data, the results being:

435W data FWHM = 0.279 +/- 0.035
814W data FWHM = 0.326 +/- 0.058

By comparison my puny telescope at sea level has an average FWHM value around 10X higher than Hubble.
A larger sample size would be preferable but the dependence of resolution on wavelength is apparent.

Irrespective of what method Lerner employs the lack of differentiation of resolution between the Hubble filtered data is telling.

Hmm ... you've convinced me, but I'm not sure if that test will make any difference to Lerner(?)

I think something a little more 'blunt' may be needed(?)

 

[SelfSim]

Oh well .. did it anyway and reposted (some) of your above testing and comments. I hope you don't mind(?)

 

[sjastro]

Oh well .. did it anyway and reposted (some) of your above testing and comments. I hope you don't mind(?)

No problems except for a minor error.
Hubble used a 475w filter instead of a 435w which means the theoretical system angular resolution is 0.066 not 0.062 arcsec.
The measured values remain the same.

Interestingly the measurements I made were performed on single exposures.
Hubble claim they can reduce the FWHM in the range of 0.1-0.14 arcsec at 370nm by dithering and stacking multiple exposures.

The WFC detector is a pair of butted (2K by 4K), thinned and backside-illuminated, SITe CCDs with a red-optimized coating, a long wavelength halo fix, and 15 × 15 μm pixels. The plate scale is 0.050 arcsec/pixel. The WFC PSF is critically sampled at 1160 nm and undersampled by a factor of three at 370 nm. Well-dithered observations with the WFC should result in a reconstructed PSF FWHM of 0.1" to 0.14".

The quote says it all for the dependance of wavelength on FWHM.
The PSF or FWHM is so small at 370nm it is undersampled yet large enough to be it critically sampled at 1160nm.

 

[SelfSim]

No problems except for a minor error.
Hubble used a 475w filter instead of a 435w which means the theoretical system angular resolution is 0.066 not 0.062 arcsec.
The measured values remain the same.

Now corrected.

Interestingly the measurements are based on single exposures.
Hubble claim they can reduce the FWHM in the range of 0.1-0.14 arcsec at 370nm by dithering and stacking multiple exposures.
...
The quote says it all for the dependance of wavelength on FWHM.
The PSF or FWHM is so small at 370nm it is undersampled yet large enough to be it critically sampled at 1160nm.

Does Lerner's method recognise this?

 

[sjastro]

Now corrected.

Does Lerner's method recognise this?

Probably not.
It raises an interesting point.
The data I used for the measurements were based on single exposures to avoid the pitfalls of multiple exposures and stacking (such as in this case dithering).
If Lerner's Hubble data for the different filters was composed of an unequal number of stacked images for each filter then the resolution will be affected by varying degrees.
Despite this I don't think Lerner's cutoff method would make any difference as it doesn't appear to measure changes in resolution in the first place.

 

[SelfSim]

It might only be temporary, but it looks like Lerner has just been suspended from physicsforums??? His name has been crossed out.
It may be a revisionism issue to do with his paper?

(All of which I consider as being most unfortunate for him .. as well as for the discussion there!)

 

[sjastro]

It might only be temporary, but it looks like Lerner has just been suspended from physicsforums??? His name has been crossed out.
It may be a revisionism issue to do with his paper?

(All of which I consider as being most unfortunate for him .. as well as for the discussion there!)

This is most regrettable.
Lerner didn't deserve it and hopefully the ban is temporary.

As a matter of interest I downloaded a dithered and drizzled five image combination of M30 with the f814w filter and compared to the single image version I examined previously.

Five image combination FWHM:- 0.110 +/- 0.005 arcsec.
Compared to single image FWHM:- 0.326 +/- 0.058 arcsec.

The five image version is now critically sampled.
This highlights the dangers of doing resolution analysis on single and stacked images which perhaps Lerner didn't take into consideration.