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Hi all,

May I add two points to this important discussion?

1. My usual point: Maybe it is relevant that when 
looking at the refection from a mirror, one has 
an essentially infinite level of signal (the 
reflection of a mW laser beam) that is millions 
if not billions of times larger than that 
available from viewing a fluorescent bead that is 
only 100 nm in diameter. Because of this, it is 
common to cylindrically average the signal in the 
case of the bead, a process that can mask the 
effect of asymmetries in the OTF such as the 
astigmatism caused by imperfect beam splitters or 
improper alignment.

Apart from this, Poisson noise will have a much 
greater effect in terms of introducing 
uncertainty..

2. My other usual point: Is spherical aberration 
involved? Beads are made of plastic and the RI of 
plastic may or may not be the same as that of the 
surrounding medium or that for which the 
objective was designed. Of course, one assumes 
that this has little effect when the diameter of 
the bead is 50nm, but as such beads usually give 
only about 1/8th the signal of 100nm beads made 
of the same material and only about 1/64th the 
signal of 200nm beads, point 1 (above) can drive 
the user to larger beads (and larger pinhole 
settings). I have no calculation to describe the 
blurring effect of using any particular design of 
bead in any specific mounting medium, however, I 
would expect such blurring to be more pronounced 
in the z than in the x-y direction because some 
of the rays from focus planes on the far side 
have to pass through the bead. This would be even 
more important is the entrance pupil of the 
objective is not fully and evenly filled by the 
laser beam.

Perhaps one should also point out the 
peculiarities of the light signal reflected from 
a flat RI interface, such as that between 
coverslip and water, compared to that produced by 
reflection from a metallic mirror. The former 
will contain proportionally more signal from 
"high-NA" rays than from those approaching the 
interface at closer to normal incidence and there 
is also the fact that the amount reflected at an 
RI interface varies strongly with the angle 
between the polarization of a high-NA ray and the 
orientation of the surface. The asymmetric 
doughnut-shaped apodization resulting from these 
effects can make the "z-resolution" look better 
(or worse) than it would be otherwise.

I can see the 
"thin-layer-of-fluorescent-immersion-oil" 
specimen being useful for measuring the 
performance of oil-immersion lenses, but how does 
one use it to measure the performance of water or 
glycerine objectives?

The 
"thin-layer-of-fluorescent-molecules-deposited-on-glass" 
specimens do not have this problem, but I would 
guess that the signal levels might be lower and 
there could be orientation effects related to the 
alignment between the (possibly non-random) 
dipole axes of the dye and the electric field 
orientation of a convergent and polarized light 
beam.

More to the point, who has compared the PSF of a 
bead near the coverslip surface with one embedded 
even a few µm inside a watery (living?) 
biological specimen? My few attempts to do so 
have revealed pronounced asymmetries that are 
readily visible by eye (as long as the eye is 
observing and the stored image collected from the 
CCD). In other words, apart from its use as a 
(very important) check on instrument performance, 
do we really need to know the PSF or FWHM etc to 
such precision?

Regards,

Jim Pawley

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>
>Reto,
>you pointed out correctly that the integrated 
>intensity in any 2d plane of a widefield PSF is 
>identical, in theory. Although, to the trained 
>eye it gives away the singularity in reciprocal 
>space, but this by itself may not fully explain 
>the sectioning capabilities. The widefield 
>microscope indeed has no sectioning ability, but 
>strictly only at the zero frequency component! 
>In other words, you can not focus on a plane 
>object or fluorescent sheet without detail. 
>However you can focus on small dust particles on 
>it that exhibit higher frequency components. 
>This all becomes clear when looking at the OTF. 
>There you can see that the "sectioning strength" 
>actually depends on the frequency and it has a 
>maximum in about the middle of the radius of 
>this torus, while as said before, there is a 
>singularity (Dirac) in its origin.
>
>Now having said that, when the bead used in the 
>measurements approximates a Dirac, its spectrum 
>is a constant, leaving the product with the OTF 
>unchanged and what you see in the inverse FT 
>simply is the PSF. It is straight forward that 
>the axial extend of that PSF corresponds to the 
>sectioning ability at around the reciprocal of 
>the pass-band frequencies of the OTF torus (... 
>and YES of a widefield microscope).
>
>I am not sure how helpful this information is to 
>some, as for specimens with varying frequency 
>content, your sectioning will vary too. Lower 
>frequencies usually dominate giving the well 
>known response and the notion of no sectioning. 
>Using deconvolution one can increase the 
>sectioning capabilities, but really only in the 
>nonlinear (iterative with positivity constraint) 
>case where the lower pass band frequencies, that 
>got lost lost due to the inner part of the torus 
>become restored, if indeed they were present in 
>the specimen to begin with.
>
>Hope that helped
>Regards
>Lutz
>
>__________________________________
>L u t z   S c h a e f e r
>Sen. Scientist
>Mathematical modeling / Computational microscopy
>Advanced Imaging Methodology Consultation
>16-715 Doon Village Rd.
>Kitchener, ON, N2P 2A2, Canada
>Phone/Fax: +1 519 894 8870
>Email: [log in to unmask]
>Website: http://home.golden.net/~lschafer/
>___________________________________
>
>-----Original Message----- From: Reto Fiolka
>Sent: Monday, October 07, 2013 10:47 AM
>To: [log in to unmask]
>Subject: Re: Using a mirror for axial resolution testing
>
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>
>Hi John
>
>This is my humble opinion:
>
>Measuring resolution with beads in a shift invariant imaging system (image is
>convolution with PSF) in any dimension is considered legitimate provided you
>are using sufficiently small beads.
>
>
>Sufficiently small: if your bead is 10 times smaller than the PSF you are
>measuring, then your error is below 1% (rough estimation assuming gaussian
>profile for PSF and bead fluorophore distribution: sqrt(1^2+0.1^2)=1.005 ). So
>a 50nm bead for axial resolution in confocal microscopy is safe.
>
>Any peer reviewed journal that I am aware of accepts such a measurment
>when you introduce a new technique.
>
>Brad Amos probably means that having a finite FWHM in the axial PSF does not
>mean that you have a good optical sectioning capability. That the widefield
>microscope has no sectioning capability is 
>included in its PSF: the out of focus
>rings conserve the same energy as is found in the focal plane, hence there is
>no sectioning. However just measuring the 
>profile along the central axis will not
>reveal this, it might actually look as the intensity would decrease as you go
>away from the focal plane.
>
>Best,
>Reto


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