HOW FAR IS THE OLD LOG AMP?
Howard Shapiro (HPANDA@HARVARDA.HARVARD.EDU)
Thu, 11 Nov 93 20:35:46 EST
Greetings, all -
There seems to be a veritable log jam on the net lately...
Log amps are most often used for immunofluorescence measurements,
and less often for analyses of material such as sea water or
urine which contain objects covering wide ranges of size, DNA
content, etc.
While immunofluorescence measurements need a large dynamic range,
they shouldn't need all that much precision, because the biology
itself gives you CV's of 20% or more. This doesn't really
deserve more than a 256-channel scale, or 64 x 64 in 2-D analy-
sis.
However, as the immunologists are now, at long last, beginning to
realize that it is better to quantify numbers of binding sites on
cell surfaces than to report "percent positive" (real progress in
this direction was reported at last week's Leukocyte Differentia-
tion Antigen meeting), we are now all too frequently encountering
situations in which people translate from "log" to linear and
back. This is risky, first because of transfer function problems
(a log amp is not a log table), and, second, because ugly gaps
crop up when low resolution data are massaged in this way.
The first step toward solving the log amp problem involves recog-
nition of the dynamic range of real data. If the noise level is
100 molecules of fluorescein, and the most abundant surface
antigen is present in amounts of less than 1,000,000
molecules/cell, you only need four decades of dynamic range. PMT
characteristics also impose a similar limit, even if the resis-
tive dynode chain is replaced by a Cockcroft-Walton circuit as
advocated in recent articles from Hamamatsu. For almost all
practical purposes, 3 1/2 good decades are fine.
Bob Auer's digital solution in the Coulter XL was essentially
forced on him by the problem of 4-color compensation. Fluores-
cence spectral overlap compensation has to be done on linear sig-
nals and, when done by analog electronics, requires that the com-
pensation circuitry be placed on the input side of the log amp.
4-color compensation ideally requires 12 op amps, which, even
with good electronic design, will almost certainly raise the
noise level at the log amp inputs above the level of 1 mV needed
to maintain a 4-decade dynamic range. The only practical
alternative is high-resolution digitization. Bob calculated 20
bits would be needed, otherwise the data at the low end would get
the jaggies. My limited experience suggests that you can get
away with 16 bit digitization because there's enough noise at the
low end to smooth out the jaggies.
The problem is then one of finding peak detectors and/or in-
tegrators which work down to 3 mV or less; no commercial systems
other than the XL meet that spec but the circuitry can be had,
and costs no more than good log amps. This is available now, and
can be used with existing 16-bit data acquisition systems; it
enables compensation to be done digitally after the fact (see
Bruce Bagwell & Earl Adams in the New York Academy of Sciences
Volume on Clinical Flow Cytometry) and allows easy, accurate
linear to log conversion by table look-up.
Doing the whole job of pulse detection and measurement of height,
width, and area by digital signal processing is just becoming
feasible now, requiring the dedication of a $300 14-bit 2MHz A-D
converter (16 measurements of an 8 microsecond pulse give an 18-
bit dynamic range) and a DSP chip or two for each measurement
channel. This should be standard on commercial systems within 5
years, by which time it will be one log cheaper. And, after all
that, it will probably still be fine to display log data on a 256
channel or a 64 x 64 scale.
Further details in the 3rd Edition of guess what book...
Regards,
Howard
CD ROM Vol 2 was produced by staff at the Purdue University Cytometry Laboratories
and distributed free of charge as an educational service to the cytometry community.
If you have any comments please direct them to Dr. J. Paul Robinson, Professor & Director, PUCL,
Purdue University, West Lafayette, IN 47907. Phone:(317) 494-0757; FAX (317) 494-0517; Web http://www.cyto.purdue.edu
EMAIL robinson@flowcyt.cyto.purdue.edu
