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Andrew, this paper might be of interest to you:

Title:
Structured illumination diffraction phase microscopy for broadband, subdiffraction resolution, quantitative phase imaging

Authors:
Chowdhury, S; Izatt, J

Author Full Names:
Chowdhury, Shwetadwip; Izatt, Joseph

Source:
OPTICS LETTERS, 39 (4):1015-1018; 10.1364/OL.39.001015 FEB 15 2014 

Language:
English

Document Type:
Article

KeyWords Plus:
DIGITAL HOLOGRAPHIC MICROSCOPY; FLUORESCENCE MICROSCOPY; LIMIT; SUPERRESOLUTION

Abstract: 
Structured illumination microscopy (SIM) is an established technique
that allows subdiffraction resolution imaging by heterodyning high
sample frequencies into the system's passband via structured
illumination. However, until now, SIM has been typically used to achieve
subdiffraction resolution for intensity-based imaging. Here, we present
a novel optical setup that uses structured illumination with a broadband
light source to obtain noise-reduced, subdiffraction resolution,
quantitative phase imaging (QPM) of cells. We compare this with a
previous work for subdiffraction QPM imaging via SIM that used a laser
source, and was thus still corrupted by coherent noise. (C) 2014 Optical
Society of America


On 2014-03-26, at 6:12 PM, Andrew York wrote:

> *****
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> Post images on http://www.imgur.com and include the link in your posting.
> *****
> 
> Hm, I should have drawn the rays differently between the annular aperture
> and the condenser lens in the phase contrast illustration. Oops.
> 
> I think this is irrelevant to my questions, though. Hope it's not a
> distraction.
> On Mar 26, 2014 3:59 PM, "Andrew York" <
> [log in to unmask]> wrote:
> 
>> Some excellent points have been raised:
>> * Deflection and optical path length differences are often two sides of
>> the same coin (Zdenek)
>> * Image brightness in phase microscopy is sensitive to reflection, in
>> addition to absorption and deflection (James)
>> ...and I'm not sure we've reached a consensus on my original question.
>> 
>> I've tried to illustrate the simplest realistic case which addresses my
>> question and avoids these complications. In the diagram below:
>> http://goo.gl/2u6DDe
>> ...my phase object is a homogenous glass slab with two raised regions. The
>> two regions have different thicknesses, (let's say 200 nm and 400 nm
>> thick). The two raised regions are wide compared to the lateral resolution
>> of the imaging system (let's say tens of microns). The raised regions are
>> perfectly smooth, with the same index of refraction as the slab. The
>> immersion medium is air. The illumination wavelength is visible (let's say
>> 500 nm).
>> 
>> My expectations:
>> The phase contrast image shows the same brightness everywhere in the
>> image, except at the edges of the raised regions.
>> The interferometric image shows a brightness which depends on the local
>> thickness of the object, three different brightnesses in this case.
>> 
>> I believe Zdenek and Shalin share my expectations. I sounds like Tobias
>> does not share my expectations, but is equally curious about the answer.
>> James, what's your expectation?
>> 
>> My questions:
>> 1. Do my expectations match reality?
>> 2. Is there any confusion or disagreement about what to expect?
>> 3. Does anyone think the phase contrast image intensity near the centers
>> of the raised regions shows which of the two regions is thicker?
>> 
>> Bonus questions: (Assuming 1, 2, and 3 are straightforward)
>> 4. Does varying the phase shift induced by the phase ring (as described by
>> Phillippe) allow image intensity near the centers of the raised regions to
>> tell us local thickness of the raised regions?
>> 
>> On Wed, Mar 26, 2014 at 11:01 AM, MODEL, MICHAEL <[log in to unmask]> wrote:
>> 
>>> *****
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>>> 
>>> Sergey -
>>> Quantitative DIC has been described in
>>> 
>>> Kou et al. "Transport-of-intensity approach to differential interference
>>> contrast (TI-DIC) microscopy for quantitative phase imaging." Optics
>>> letters 35.3 (2010): 447-449.
>>> 
>>> For quantitative brightfield also look for "transport of intensity".
>>> 
>>> There is also a method called "defocusing microscopy", I don't know much
>>> about it.
>>> 
>>> Mike
>>> 
>>> -----Original Message-----
>>> From: Confocal Microscopy List [mailto:[log in to unmask]]
>>> On Behalf Of Sergey Tauger
>>> Sent: Wednesday, March 26, 2014 10:45 AM
>>> To: [log in to unmask]
>>> Subject: Re: Phase contrast microscopy
>>> 
>>> *****
>>> To join, leave or search the confocal microscopy listserv, go to:
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>>> 
>>> Hi,
>>> 
>>> Mike, Phillippe, could you please share the article names of quantitative
>>> phase contrast, brightfield and DIC? I cannot find any articles neither
>>> that prove the methods are quantitative, nor PSF for the methods.
>>> 
>>> Best,
>>> Sergey
>>> 
>> 
>>