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Hi, Jeff

The concept is really quite simple. Darkfield doesn't "block" the 
light.  Rather, a darkfield system "conditions" the light. This is a 
bit difficult to do without a diagram, but let's try.  First:  There 
are two lens systems involved:  The condenser and the objective.

Step 1: The optics
Imagine light approaching the CONDENSER in a bundle of parallel 
rays.  The curve on the incoming side of the condenser causes the 
light to emerge at  wide variety of angles (You can prove this by 
moving objectives out of the way and placing a business card on its 
edge over the condenser.  P. S. - open the condenser aperture fully 
for this experiment).  Light coming through the center "sees" the 
flat tangent of that curve so continues straight on.  Light coming 
through the edges sees maximum angle of that curve so is bent at a 
high angle.  The higher the NA of the condenser, the broader the 
range of angles emitted from the condenser.  To simplifiy, use the 
optic axis as 0o (zero degrees) deviation.  Hypothetically, the 
maximum angle emitted would be +/- 90o.  (Interesting experiment: 
test the effect of opening and closing the condenser aperture on the 
angle emerging from the condenser.  Second experiment: if you have a 
turret condenser, close the aperture and very slightly rotate the 
condenser so that the light approaches from other angles. Use the 
card to watch what happens to the angle).

On the receiving side, the OBJECTIVE will collect a range of angles 
set by its numerical aperture (NA = n sine a, where n = refractive 
index of the medium between the top of the sample prep and sine a = 
sine of half the collecting angle).

Step 2: The sample
Light emitted from the condenser interacts with the specimen in a 
variety of ways (diffraction, refraction, reflection, fluorescence, 
etc.).  The objective collects that light to form the image ("light 
is the messenger").  In the simplest terms, the image is formed by 
the interference between the undiffracted background light and the 
diffracted light from the specimen.  The undiffracted light is 
responsible for the background of the image;  the diffracted light 
contributes to resolution, edge fidelity, and intensity of the sample 
detail.  Part of the image is also be formed by interference between 
specific of components of the diffracted light, but will not 
contribute to the background (a further discussion is beyond the 
scope of this posting).

Step 3: Enter Darkfield
The goal of a darkfield system is to select, at the condenser, only 
those peripheral rays which will emerge at a very high angle.  We 
want to select those rays of light which will have such a high angle 
that they will miss being collected by the objective.  Since this is 
undiffracted light, it contributes to the background information in 
the image.  If we don't collect it (zero light), the background will 
be black (hence, the term "darkfield").
As in all imaging, some of this highly angled light WILL interact 
with the specimen.  It will be scattered at the appropriate angles to 
be collected by the objective and go on to form an image.

There are two general approaches for engendering darkfield 
microscopy:  A central patch stop to block all rays except those 
highly angled peripheral rays or a highly curved, hemispherical 
mirror mounted in the condenser, which will reflect light at very 
high angles as it emerges from the condenser.  The first approach 
creates angles effective to generate darkfield with lower NA 
objectives (about 0.15, associated with magnifications up to about 
10x).  The more elaborate mirror systems use oil immersion both 
between the condenser and the back of the slide and the top of the 
prep and  the objective) and are effective for higher NAs (~1.4, 
associated with 60x or 100x oil immersion objectives).

Regarding the smallest object you can "see":
Darkfield is limited by DETECTION (how many photons of light can be 
scattered to form the image) not RESOLUTION (based on diffraction and 
the interaction with the undiffracted + diffracted light).  The 
detection is limited by the light (quantum) efficiency of your optics 
and camera and, for direct viewing, your eye.  Since your eye can 
detect just a few photons, using darkfield (especially the oil 
immersion variety) you will be able to "DETECT" objects as small as 
about 50-60nm.  You won't be able to define their size or tell much 
about their shape or edges (parameters inherent in resolution), but 
you will be able to tell that something is there.

ARTIFACTS:
1. Because the photons are coming to you from throughout the entire 
depth of the sample ("infinitely great" depth of field), unless the 
sample is thin, darkfield images will often be "busy" with images 
from one plane overlaying images from those above and below.
2. Because you are using a very narrow range of angles to illuminate 
the sample, the light is highly coherent, so you will see a lot of 
internal diffraction effects ("ringing" around the edges)
3. Because scatter is the main source of the imaging information, you 
will also see lot of local chromatic aberration (rainbows or colors 
at the edges).  For that reason, we always recommend that you view 
the sample in brightfield first to asses if color is real or just an 
artifact of darkfield.

SEVERAL OTHER THINGS TO CONSIDER:
Other imaging techniques remove the undiffracted, background-forming 
light, but other imaging parameters are in operation which determine 
whether they are diffraction or detection limited.
EX 1: Polarized light (which IS diffraction limited)
EX 2: DIC (which is based on polarized light)  (which is also 
diffraction limited)
EX 3: Fluorescence (which is detection limited)
EX 4: CytoViva (cytoviva.com) use a darkfield condenser in a novel 
way which (a) actually improves resolution and (b) improves optical 
sectioning.  It does so by placing the light source essentially at 
the front focal plane of the objective, changing part of the normal 
darkfield optics.  As a result, it can actually RESOLVE fine detail 
on the order of 90 nm (my old eyes resolved at the 90nm level; the 
younger tech specialist which whom I had a chance to work early on, 
could resolve about 82nm on the Richardson test slide).   And, unlike 
darkfield, it CAN optically section.  Also, more recent work suggests 
that it does not suffer from the chromatic effects of conventional 
darkfield and, as a result, has been having considerable success in 
hyperspectral imaging.  So, even though a darkfield condenser is 
involved and even though the image has a dark background, its 
behavior and capabilities put it into a category of its own.

  By the way, you can create your own darkfield patch stops using 
India Ink on overhead transparency film.  To determine the size of the patch:
1.  Set up Koehler illumination then move to a clear part of your slide
2.  Remove the eyepiece and peer down the tube into the back focal 
place of the objective (BFPo)
3. Close the CONDENSER aperture until you can just barely see the 
edge of its leaves in the BFPo)
4, Gently remove the condenser from the microscope, flip it upside 
down, and measure the size of the opening of the aperture. That is 
the size you need for the patch stop.
(Luckily, the manufacturers make these available for very little money).
5. To operate: make sure that the  patch stop is in the Front Focal 
Plane of the condesner (in the location of the aperture iris.

Also something fun:
Rheinberg illumination was an important contrast technique in the mid 
1800's and is derived from the same principle but uses colored patch 
stops instead of black.  With a black patch stop on a white 
background, you get white images on a black field;  With a green 
patch stop on a white background, you get white objects on a green 
field.  One of my favorites is a blue patch stop on a yellow 
background, which gives you yellow objects on a blue field (a highly 
effective contrast combination for the human eye).   I once taught a 
week long course for a company to whom  counting filamentous mold was 
important.  One of the biggest successes came by accident when we 
used Rheinberg with their samples.  This combination made mold 
counting really easy!  One note: you can make Rheinberg filters from 
any colored plastic film but may need to (a) use a double thickness 
to get good rich color and (b) crank up your light source.

Hope this is all helpful.

Good hunting!
Barbara Foster, President & Chief Consultant
Microscopy/Microscopy Education*
www.MicroscopyEducation.com

*A subsidiary of The Microscopy & Imaging Place, Inc.
7101 Royal Glen Trail, Suite A
McKinney, TX 75070
P: 972-924-5310
F: 214-592-0277

MME is currently scheduling courses for now and through June 2015. 
Call us today for a free training evaluation.






At 04:19 PM 1/30/2015, Jeff Spector wrote:
>*****
>To join, leave or search the confocal microscopy listserv, go to:
>http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
>Post images on http://www.imgur.com and include the link in your posting.
>*****
>
>Greetings,
>    Can someone please point me to some references involving the theory
>behind darkfield microscopy? I understand the basic idea, but all I can
>find are different iterations of the basic idea that you block most of the
>light and only image scattered light. I'd like to learn a bit more about
>technical aspects of  darkfield, i.e. what is the smallest object you can
>observe? What role do illumination power and camera exposure play in the
>quality of the final image. What role does specimen thickness/size play in
>the final image and can you discern objects of different size
>etc...
>Any help would be greatly appreciated. Perhaps I simply need to read up on
>scattering theory?
>thanks..
>-jeff