The Weave on the Epson 4800 Printer
by Gerry Eskin, Sept. 2009
Introduction
Inkjet printers have a printing head with an array of nozzles. In the case of the Epson 4800 printer, this array has 180 columns and 8 rows.
Link to Epson 4800;
Other printers with this configuration include the Epson 3800, 4880,7800,7880,9800 and 9880.
Link to other Epson professional printers
Looking at the 4800 printer from above, the paper is positioned so that
the top of the page comes out of the printer in the front. The dotted
line on the drawing marks off the area that cannot be printed. This is
about 1/10" on the top and sides and larger on the bottom.
Papers placed under a printing head. The paper moves to a position where the head can print the top of a vertical page first. The paper's initial position is set by the print driver by the setting Position-Top.
The Head moves across the paper from left to right and, with the setting High Speed Off setting, only prints in one direction.
Each column on the head prints a different ink. The 180 nozzles available to print each color are spread out over an area of approximately one inch(vertical). But here is a problem - 180 dots per inch (dpi) is not enough to produce good photographic prints. Good quality requires at least 720 dpi vertically. Epson claims to be able to do this. So how do they use a head with 180 nozzles spread over one inch to get a print with 720 dpi?
How the printer fills in the space between the natural nozzle placement is called the weave. I have often wondered how this was done, but have had difficulty in finding written information on the subject. There are things written on how this should be done, but I have not found detailed information on how this is actually done.To help answer this question, I have spent numerous hours running test son my printers, the results of which are reported here.
Most of the work reported here has been done on the Epson 4800, some of the results have been replicated on the 3800. I leave to the end of the paper, conjectures on how much of this may apply to other printers.
Study Set Up
Inkjet printing is done by moving paper to a fixed position, discharging ink(from some of the nozzles), advancing the paper to a new position,firing again, etc.
Our goal is to find out the size of each of these paper advance and how many nozzles are fired after each advance. As a first step, we construct a test image which will exercises as many nozzles as possible. The image created for this purpose, is a patch of all black (k=100), a one inch square. When printed as "black only" at 1440 x 720, all black nozzles should fire in every horizontal and vertical position (with some Exceptions).The problem will be to isolate which nozzles fire on each paper advance and the size of each paper advance. We approach this by stopping the printer after each carriage return and studying, with the aid of microscope, what new pattern has been printed (for details see 1.0 Methodology).
When printing at the 1440x720 setting, a primary job of the weave is to fillin each 1/180 blank space with 3 lines of dots to reduce the spacing to1/720. The primary method used involves Paper Advances (PA)that are not evenly divisible by 1/180. The size of these advances turnout to be just a little larger than the space between 10 nozzles.(10 x1/180"). To be more precise the advances are alternating values of42/720" and 41/720". Near the upper margin of the paper a slightly different weave is used.
The Basic Weave
The vertical weave is achieved by advancing the paper some 42 line (line are spaced 1/720"),printing 177 nozzles, then repeating the process for a 41 step advance.This process is repeated until the print is completed.
Here are a formal set of rules that produce the complete print.
Rule 1 - Fire177 adjacent nozzles vertically, advance the head 1/360"horizontally,fires again, advances again, etc until the left edge of the image is reached. Return the head to its left most position.
Next,advance paper 41/720", fire he nozzles, advance the head 1/360"horizontally, fires again, advances again, etc until the right edge of the image is reached (then return head)..
Next, the paper is advanced 42/720", nozzles are fired, the head advances 1/360" horizontally, fire again, advances etc.
This alternating pattern is used until the print is complete.
Rule 2 - Feather the first and last 11 rows of each print
Rule 3 - Do not print any dots that fall into a margin area.
Rule 4 - In area very close to the upper edge of the paper modify rule 1 as described in Special Case.
For more details in this description, see the Appendix in general and note Excluded Details.
Example
To
print the 1" black patch takes 32-34 paper advances. We start by taking
a look at the pattern made in the middle of this sequence choosing an upper
margin that is outside of the Special case region. The margin setting we use is Position- Top = .986".
To the right is a set of photograph (taken through a microscope) of dot placements after the paper has been advanced 15,16,17,18 and 19 times.The blue ruling lines (superimposed on the image) show distances of4/720", namely the vertical distance between the nozzles).The numbers in the side margins are scale values where 720 lines =1".
Looking first at paper advance 17 (PA(17)),printing starts at line 14 and ends at line 714. 177 horizontal lines of dots are printed. Most of the dots are adjacent to one another but there are holes in the first and last 11 rows as is required by rule-2. PA(17) advances by 41 lines from PA(16), a result that is consistent with rule-1.
Advances 15, 16, 18 and 19 are all truncated in a manner consistent with rule-3. All advances shown are consistent with Rule-1.
Feather
We
noted above that the usual horizontal advance is 1/360". For the first
and last 11 lines the advance it is not always 1/360. At the very top
and at the very bottom there are fewer dots on a horizontal line. As it
goes inward there are more dots. This spread at the end points is the
feather pattern.
Here we look again at the print after PA(16). The lower feather is shown to the left (in black). The beginning of PA(32) is shown in red. Where the first leaves off the second begins. They are compliments.
The feather pattern is used for two purposes. It provides a smooth transition where one print from the head stops and another begins. It also solves a problem resulting from the 41/42 alternating pattern used in the weave. Without feathering, some horizontal lines would receive more dots than others. Every 4th row would receive 5 hits rather than the four all other lines receive.
For more details see 4.0 Feather.
Special Case - Printing Near the Upper Edge of the Paper
The patterns described above, of printing 177 nozzles after alternating paper advances of either 41/720 or 42/720, is the case for all upper margin greater than about an inch(more precisely ( Position-Top setting of .916). Prints with less upper margin use a modified procedure. This involves a combination of smaller paper advances and printing a variable number of nozzles.
Below is a schematic of the process for Position-Top=0.To the left is a schematic of this pattern assuming the print starts as close the upper paper edge as Epson will allow (this is labeled Position-Top =0) Although "0" is the first line that can be printed without the borderless setting, it actually starts printing at .111" from the top of the paper.
22 nozzles are fired to make the first columns of the print.
PA(1) advances 2/720 and the number of nozzles printed is 33.
PA(2) is 5/720 and the of nozzles printed is 43.
This pattern of small advances (two or fives) is used until at PA(15) we run out of nozzles and must start using the larger advances to maintain the pattern. From PA(16)onward the weave is the same as that described above, namely advances of 41/720 and 42/720 and the printing of 177 nozzles after each advance.
For more detail see, Position-Top=0.
Filling in the Vertical Pattern
We
are interested here in how many different advances result in printing on
each vertical line. If the answer is 2, it is a 2 pass weave. If the
answer is 4, it is a four pass weave. Unfortunately it is just a little
more complicated than this.
Shown above is the early dot pattern for a margin setting of .1667 (this starts printing on line 120 of the printable area).
Line 120 receives dots from PA 0,3,8,11,16
Line 121 receives dots from PA 1,6,9,14
Line 122 receives dots from PA 4,7,12,15
Line 123 receives dots from PA 2,5,10,13
Lines 121,122 and 123 receive dots from 4 PAs but line 120 appears to receive 5. But note that PA(0) and PA(16) are prints with the feather pattern. The two PAs combined contribute the same number of dots as each of the other PAs. The general pattern is that for every block of 4 lines, 3 out of the 4 obtain contributions from 4 PA's and 1 obtains contributions from 5, but with 2 being of the feathered type. On net the pattern provides a full 4 Pass Weave.
Other Printers
I have replicated some of the above analysis on the Epson 3800 with the following results:
The basic weave is the same
The feather is the same
The special treatment near the top of the page is not used.
i
have not studied other printers but would conjecture that if the head
for another printer has the same number of rows (180) then it may use
the same weave. As mentioned previously 180 line heads are used on
the4880,7800,7880,9800 and the 9880. If the head has more or less
heads(like the 9900) the weave needs to differ in some way.
In the main paper we provide only enough details to illustrate the general nature of the weave. Here the treatment is more detailed.
1.0 Setup
1.1 Terminology
The head moves only horizontally and in the case of "High Speed Off" prints only in one direction. First, the paper is set in a position determined by the setting - Position- Top= x.xxx ( hereafter called PT), the smallest margin is obtained at PT(0). "0"means the closest to the top of the page that the printer will allow without the borderless setting. The size of this margin is 1/720"= 0.111".Once the paper is set, the head discharges ink out of some of its nozzles. In the case of "Black Only"and full black (k=100) almost all of its 180 nozzles are fired. After printing the head moves 1/180" to the right and fires again. This process is repeated until the right edge of the printable area (or left end of the image is reach). We will call this initial paper setting PA(0) and the number of nozzles that fire after this PR(0), e.g.- for PT(0), PR(0)=22. After this initial printing and a carriage return, there is a paper advance and another print. This first advance we call PA(1) and the print that follows PR(1). For a one inch image there are about 34 advances and 35 prints.
1.2 Printers, Settings and Targets
Printer- Epson 4800 (some steps are replicated on the 3800)
Dpi setting-1440 x720 (unidirectional- high speed off). Dpi is now labeled in the printer settings as"quality" and the value we are talking about is labeled superfine-1440. Superfine-1440 means, 1440 dpi horizontally, 720 vertically and uses the weave we are discussing. Our interest is primarily in the vertical weave, this being 720dpi.
Color- Black (only)
Target- A black patch (k=100) of size 1" x 1"
1.3 Methodology- It
is difficult the "see" the details of the dot patterns made by the
head. The dots are quite small and they are printed almost on top of
each other. To deal with the size various enlargement instruments are
used including a macro lens (1:1) on a digital camera, a digital
microscope and a high resolution scanner. When it is necessary to
examine a larger area than can be covered by these devises, the various
images are stitched together using the Photo Merge procedure in
Photoshop.
1.4 Isolation Techniques
1.4.1- Mark Paper Advances- The number of paper advances and their approximate size can be measured by drawing a line after each print. There are various ways to do this. On the 4800, one way is to open the printer cover, disable the"cover open" reader and record advances against one of the leftmost flat roller wheels. I do not conjecture what, disabling the cover open reader, does to the warranty.
1.4.2-Print and Stop technique
1.4.2a- Cumulative Prints after PA(x)-we are interested in seeing what is printed after a specified number of Paper Advances PA(x). To see this we stop the printer after a specified number of PA's and enlarge the resulting print.
1.4.2b- Non Cumulative Print after PA(x)-To more clearly see the structure of the weave we modify the above printing method. First we allow the printer to make N paper advance ,print the Nth step and stop the printers. This is the same procedure as used above. The new step is to then put a fresh piece of paper in the printer and allow it to print one more line. This latter print prints only nozzles fired during this N+1 pass.
2.0 Characteristics of the Head
Many of the characteristics of the head can be seen from a nozzle check pattern.
The entire Black section of the nozzle check is displayed in the left portion of the image below. To the right is a one inch rule marked to 1/32 of an inch. in the center of the image is the Non Cum Print for a case where there is no truncation of the print due to margins.
By counting the "flats" it can be easily verifies that there are 180 black nozzles on the head.
By comparing the one inch marker to the 180th head it can be determined that 180 covers a space just short of an inch (the distance is in fact 717/720"
Next to the non cum print are bars measuring 10 nozzle distances. This shows177 nozzles firing (not the 180 that are possible). Usually, no more than 177 nozzles are fire after any given paper advance.
3.0 Basic Weave
The head has 180 nozzles per color, spaced at intervals of 1/180. Most commonly photo printing is done at 720dpi vertically. The weave issue has mostly to do with how to fill in these spaces between the natural pattern of 180 dpi. The most obvious way would be to first print the180 nozzles, then advance the paper by 1/720, print, then do this two more times, hence completing a patch at 720dpi that is about 1 inch high. Then this process could be repeat the requisite number of times to complete the print. Although this is A Way, it is not a Good way and is almost guaranteed to produce banding. The more advanced approach is to weave together the entire dot pattern. We now explore how this is done.
3.1 Paper Advance Pattern
The paper advance pattern is the most important determinant of the weave, particularly in areas away from borders.
As a 
first look at this we use the Mark Paper Advance method. A 1" black patch is printed using PT(.972). This setting is well away from the upper margin hence does not involve the special case weave.
During the print, each time the head advances, we mark a line indicating this advance, that is, we mark each PA, as shown to the right. The first mark is for PA(0), that is the first print before the paper is advanced at all.
Although we are printing only a one inch target, the paper advances
cover almost2
inches indicating that some of the advance is taken up in margin areas.
There are some 35 (34 paper advances) lines needed to print the 1"patch and
these are roughly equally distances between the advances.17of
these advances accrue in the first inch and all are print by a little
over 1 7/8" (1.875). This makes the average distance between advances,
a little more than the distance between 11 nozzles(10/180=40/720). To
refine this measurement is the purpose of sections 3.2 through 3.5.
Here we look at the characteristics of the paper advance directly by printing Cumulative Prints after PA(x).There are 35 such advances (including the initial paper placement), but in this image we only look at the cumulative advances printed after PA(0), PA(1) … , PA(17).
It can be seen that for each new paper advance and head discharge, more ink is laid down and the image gets darker. Ten more nozzles are used on each advance,ten nozzles being a distance of 10/180" or 40/720.
To increase the precision of this measurement we enlarge the first three columns.
3.3 A closer Look.
The first column shows the print before any paper advances, that is PA(0). This shows 3 rows of dots. PA(1) shows 13 new rows of dots plus, the 3 rows from PA(0). PA(2) shows 23 rows of dots plus the dots printed after PA(1).
The advance shown in the second column is a little larger than the distance between 11 nozzles ( the distance between nozzles vertically is 1/180).More precisely the advance is 1/4th the distance between dots, hence 41/720.
Reviewing the print after PA(2) we see a similar but not identical outcome. The advance is 10 nozzles plus half the distance between nozzles, that is, 42/720.
3.4 Aligned Advances
In
hopes of generalizing we align the leading edge of more of these
advances. Now we look at advance 13 through 17.Again we see advances
of41/720 or 42/720. Furthermore these values alternate.
A microscopic enlargement, of the top and bottom sections of a Non Cumulative print are
displayed in the main paper for advance 15 through 19. For detailed
image showing all nozzle discharges for all Paper advances (for
PT(.976) click Here.
A view of the general feather pattern is displayed in the main text.Here we measure some detailed characteristics of the feather.
Here is an enlarged print of the last 14 nozzles with column and row markers. Black lines are spaced at 1/180". Red lines divide this area in half.
The top lines has dots in almost every position, a dot every 1/360". At the bottom many fewer dots are printed. In the mid section about half the horizontal locations has dots. At bottom the count is about one out of four. Counts are displayed to the left of the image.
The 11 nozzle feather at this leading edge of the head are match by an identical pattern on the trailing edge. When the trailing edge of print is combined with the leading edge of the print after the next paper advance all of the 360columns per inch are filled in
5.0 Weave Near the Upper Border
The weave used near the upper border is a little different than elsewhere.
5.1 The 0.167 starting point
A clue about this can be seen from the Paper Advance Marks for a small margin setting (PT(.166)).This
particular setting is interesting in that it match the margin that
would be obtained by an 8x10 image printed on an 8.5 x 11" paper with
the setting-Position-Center Image.
Our marks looks quite different than the marks for the previous case studied (PT(.972)).There we saw some 35 line with similar spacing between them. Here we see20 lines that are similar to the previous case and an additional wide line. When I marked this case, I made 35 marks. Clearly 15 marks are too close together to show separately. We know that the separate lines have an average interval of 41.5 and we observe that the solid area cumulatively covers about this same distance (if you account for the thickness of the pencil lines). Thus the 14 advances are about41.5/720=3.2 apart .
The main point is that the weave pattern in this area cannot be based on a41/720-42/720 Paper Advance. It must be much smaller, something with an average advance of about 3.2.
5.2 Other starting points
The chart to the right shows Paper Advance Marks for a rang of Position-Top settings.The top row is the PT(.972) case discussed previously. For this setting. all the advances are of the regular type, alternating advances of 41 and 42.
The next to the bottom row is the PT(.167) case discussed immediately above.
In has some 14 special advance.
Looking over the other cases we see a pattern. For small borders there are more special case advances than for larger borders.The most special case advances are at the 0 and .167 settings.
The use of special case advances deminishes as the margin increases in size. At PT(.944) only regular advances are used.
5.3 The Size and Character of the Special Case Advances
To measure the distance between these small advances some marking device smaller than a pen or pencil is required. A small needle does the trick.With it we can get separation.
To the right, four sets of two paper advance marks (done with a small needle) are shown. They show measurement variation but do illustrates important general points
(1) the average advance is 3.7
(2) the smaller of the two advance averages 2.1 and the larger of the two averages 5.3.
There are only a small number of advance patterns (with small average advance) that will also blend well with the regular(41/42) pattern.These are:
1/720, 2/720
1/720, 6/720
2/720, 5/720
2/720, 9/720
The first case has an average that is too low (1.5) and the last case has an average that is too high (5.5). As we do not observe any advances as low as "1" in our sample of four, we conclude that it is more likely that the 2/5 is used than that the 1/6 is used.
We do not view these four observation as conclusive on this subject, but the main point is not in doubt. Special advances are quite small and most of the dots associated with them come from printing more or less nozzles, not from variation in paper advances.
6.0 The complete Weave for starting points near the Top Edge of the Paper
To this point we have discussed features of special weave patterns. Here we present information on some complete weaves.
6.1 Position Top=.167
|
The first print PN(0) occurs after the paper is set to line 120, three nozzles are fired. The nozzles are located on lines 120,124 and 128. PA(1) is an advance of 2 lines and 13 nozzles are fired. The next advance is 5 line and 23 nozzles are then fired. |
These early advances are special case advances, they are either of size 2 or 5 and they are combined with printing variable number of nozzles. Special advances continue to be used until PA(15),at line xxx, at which point all remaining advances are of the regular type and all 177 nozzles are fired on each advance until the point when firings are limited by the bottom border of the image. For our image that is just 1" in length, the lower margin starts to play a role on PA(18). The print stops at line yyy.
A generalization of this pattern is that for any starting point below.930, all advances are of the special type until line zzz is reached.All remaining advances are of the regular type.
An image containing the complete schema for the .167 case can be obtained by clicking HERE.
This is an interesting case in that it used the greatest number of special case weave. Also the upper border does not block out a large number of nozzles. Another interesting feature of this case is that weaves for other PT settings can be deduced from this pattern.
The print starts some 80 lines from the top of the paper (.111 inches).The first discharge from the head prints 22 dots. The print starts on line2 (the first printable line being numbered "0". The first 8 nozzles are located in the margin area hence are not fired. Of these eight, three are shown on the schematic in gray to indicate that these nozzle are not normally used.
The
weave proceeds using the 2, 5 advance pattern until PA(15). after
PA(15) the weave switches to the 42,41 pattern until it is completed
after PA(32). Another interesting feature of the print is that
PR(15)=178, the only case I know of where 178 nozzles are fired.
 Click on image to see it full size (4x) |
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| Notes on the chart The full schematic for PA(0) and the other 32 paper advances required to print our 1" patch are displayed in the middle of the exhibit. To the right of this is shown photographic images of the first 20 columns of Print (produced by the Non Cum Method). Printed nozzles are shown in black except for feathered areas which are shown in blue. Red dots are position counters (every ten nozzles).Top and bottom margin areas are overlaid with yellow. The light green overlay covers the area excluded by the special rules for printing near the top of the page. For a generalization of this image see section 8.0. |
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6.3 Other Starting Points
PT(0) and PT(0.166) have been discussed above. Some information for other starting points is presented in 7.0. For information on starting points not covered above or in 7.0 see the ancillary page and the download available in 8.0.
7.0 Misc Information
To this point we have discussed the general characteristic of the weaves and given some example of complete weaves. No rules have been given for determining the number of nozzles printed at PR(0) or how to determine whether the first advance will be 41 or 42 ( or 2 v 5). Information on these issues can be determined for the schematic in 6.1. We also layout some of this information below.
7.1 Initial Print and Related InformationWe noted that for PT(.166) and PT(.972) three nozzles are printed after PA(0). Three is not always the starting value however. In general the starting value depends on the PT setting. To illustrate this we show below a number of upper margin settings both for "small" margins and for margins in the neighborhood of one inch.
| START LINE | Position TOP | PR(0) | START LINE | Position TOP | PR(0) | |
| 0 | 0 | 22 | ||||
| 1 | 0.0139 | 20 | ||||
| 2 | 0.0278 | 17 | ||||
| 3 | 0.0417 | 15 | ||||
| 4 | 0.0556 | 12 | ||||
| 5 | 0.0695 | 10 | ||||
| 6 | 0.0834 | 7 | 712 | 0.8888 | 7 | |
| 7 | 0.0973 | 5 | 713 | 0.9027 | 5 | |
| 8 | 0.1112 | 2 | 714 | 0.9166 | 2 | |
| 9 | 0.1251 | 10 | 715 | 0.9305 | 10 | |
| 10 | 0.139 | 8 | 716 | 0.9444 | 8 | |
| 11 | 0.1529 | 5 | 717 | 0.9583 | 5 | |
| 12 | 0.1668 | 3 | 718 | 0.9722 | 3 | |
| 719 | 0.9861 | 11 | ||||
| 720 | 1.0000 | 8 | ||||
| 721 | 1.0139 | 6 | ||||
| 722 | 1.0278 | 3 | ||||
| 723 | 1.0416 | 1 | ||||
| 724 | 1.0056 | 9 | ||||
| 725 | 1.0069 | 6 | ||||
| 726 | 1.0083 | 4 | ||||
| 728 | 1.0111 | 1 |
7.2 Cum PR(1) Prints and Apparent Values of PA(1)
Below are shown Cum PR(1) prints for a number of PT settings. In the case of large margin settings (PT> 0.930) the size of the Cum PR1) print allows a direct calculation of the advance. For smaller PT values this is not the case as the apparent advance is made up of two factors: the actual advance PA(1) plus a variable number of nozzles being fired. For the special case advances, the PA setting are shown in parentheses next to the observed values.
8.0 Generalization
All of the above results can be
encapsulated into a single schematic. The beginning of the schematic
for two Position-Top values is shown in an ancillary page.
The full schematic is too detailed to be viewed here, but is contained
in an image that can easily viewed in Adobe Photoshop. To download this
click HERE.
- - -
Other Notes
"Our" - Excuse my switch to the editorial "we". 
"With Some Exceptions" -Normally we would think of pure black being make up of a pattern where every available spot is filled up with a black dot. In the case of Epson printers a few of the position are not printed. One reason for this is to avoid over inking. The number of unprinted spots can be controlled by Custom/Advanced/Paper Config/Color Density slider. We leave the slider at its default setting.
"Approximately one Inch"- We claim that the regular weave pattern is used for all upper margins(Position-top) of an about an inch or greater but a more precise claim is 0.98611". This is 710/720". All paper positions are rounded Down to even 720 fractions of an inch, expressed in the print window to three decimal points. Unfortunately there is a little glitch in the program which can get the assignment a little off. The problem can be avoided by always entering a number a little larger than the desired margin.For example entering .986 will result in the margin 0.972 but entering 0.9865 will get the correct margin size.
"With one exception" - The only case I know of where more than 177 nozzles are simultaneously fired is in connection with Position Top=0. Here after PA(15), 178 nozzles are fired.
A close look will indicate that the advance is just a little bigger than this by either one quarter or one half of the distance between nozzles.Thus the advances are either 41/720 or 42/720.
It can also be confirmed that the advances alternate between these values.This can be more easily seen in the following two prints.
"Some Excluded Details"
-The head does not always print 177 dots mostly because it runs into the upper or lower margin.
-The
first Paper advance is not always 41/729", sometimes it is 42/720".When
each is used, is treated in more detail in the Appendix.
last edit: 1jan10 -even, 26Oct2009 - howie