what is the concept of N-channel geneChip? I can understand two-color and one-color(Channel) gene chip; but there is another type of gene-Chip called "N-channel chips" ; I do not know how can several (> 2) samples be hybridize in one chip. I cannot find some reference for the a material for this concept. See the following code that it has two channels "E“ and "Eb"; what does that channel mean? The expression matrices seem to have the same dimension. In my understanding, the two-color or two-channel microarray is to combine two samples (treated vs. control) in a chip, and the log(ratio) is used to express the differential expression.   

AE1548 = getAE("E-MTAB-1548", 
               path="/Users/zhang/Documents/2020/GEOsepsis/Data",
               local = TRUE, sourcedir = "/Users/zhang/Documents/2020/GEOsepsis/Data",
               type = 'full')
AE1548raw = ae2bioc(mageFiles = AE1548)#established from raw data; multi-channel data
AE1548expr1 = assayDataElement(AE1548raw,"E")
AE1548expr2 = assayDataElement(AE1548raw,"Eb")
  AE1548expr1[1:5,1:3]
  SIRS_18exp2 SIRS_19exp2 SIRS_23exp1
1    273812.0     97733.5      205330
2        41.0        26.5          50
3        42.5        25.0          48
4        40.0        23.5          49
5        38.5        24.0          53
  AE1548expr2[1:5,1:3]
  SIRS_18exp2 SIRS_19exp2 SIRS_23exp1
1          25        18.0          36
2          25        18.0          37
3          25        18.0          38
4          25        19.0          37
5          24        18.5          37
This is a mere long comment, which may help, but I do not know the details required for the answer.

Several (> 2) samples hybridized in one chip

A traditional microarray has two parts, the mobile target, which is the labelled sample, and fixed to the filter paper, glass or doped silicon is the probe, which is not labelled and is in vast excess. You can label the target fluorescently with one of a variety of fluorophores, or with different radioisotopes, which have different energies. Nobody uses radioisotope microscopy for this except for the most obscure method, say nuclear run off assays, but I mention this just to cover all bases.

Whereas you can buy whatever fluorophore you wish, the detecting machine needs to be set up for it with lasers, beam splitters and filters. Most florescent confocal microscopes use a LED lamp, a splitter and a loads of cubes of filters. In the case of flow cytometry, you can get over 16 fluorescent channels at the same time. However, deconvolution becomes necessary when one channel "bleeds" into an other —I am not sure how one deals with it with a microarray, I suspect before the step to remove regional biases (the step with LOESS regression or similar).

Affymetrix Gene chip (R)

Now, in the case of an Affymetrix Gene chip, I do not know if there is a multichannel machine, but it could be custom build. The spots on an Affymetrix chip are 3-5 µm, so regular microscopy optics still work. Although the silicon base is not transparent like a home made slide or an Agilent microarray (if these are still made). Hopefully, someone else can answer about Affymetrix machinery!

Statistics

I am not familiar with why or how you would analyse a 3+ channel experiment. One guess could be to do a dose-response experiment. But there will be some problems:


The dye flip correction would be an issue for greater than 2 samples
Channel deconvolution may be required for dyes with overlapping spectra.