EP3597439A1

EP3597439A1 - Method for measuring medium advance in a printer

Info

Publication number: EP3597439A1
Application number: EP18184379.8A
Authority: EP
Inventors: Tom J.H CLABBERS
Original assignee: Oce Holding BV
Current assignee: Canon Production Printing Holding BV
Priority date: 2018-07-19
Filing date: 2018-07-19
Publication date: 2020-01-22

Abstract

Described is a method for measuring medium advance in a printer by printing and scanning a pair of reference marks, comprising the steps of printing, in an initial procedure, at least a first initial swath of information and a second initial swath (I4) of information; including in the first initial swath a plurality of first initialization marks (10b1, 20b1, 30b1, 40b1) each printed with a different array of printing elements; including in the second initial swath a plurality of second initialization marks (10a4, 20a4, 30a4, 40a4) each printed with a different array of printing elements; for each array of printing elements used, determining a relative position of a first initialization mark and a second initialization mark printed with the array, and determining the medium advance based on the relative position of the two reference marks, taking into account a relation between the relative position of the initialization marks printed with an array of printing elements used for printing the reference marks and the relative position of the initialization marks printed with at least one further array of printing elements.

Description

FIELD OF THE INVENTION

The present invention relates to a method for measuring medium advance in a printer.

BACKGROUND ART

A scanning-type inkjet printer comprises an inkjet print head mounted on a carriage arranged to move relative to a recording medium along an axis of carriage motion while being guided by a guiding structure. A swath of information can be printed onto a recording medium by an array of jetting nozzles of the print head ejecting sequences of ink droplets towards the recording medium while the carriage is moving. A driving device is provided for driving a recording medium to move relative to the guiding structure along an axis of medium advance normal to the axis of carriage motion. By a recording medium being moved to advance over a certain distance in between the printing of a first swath and the printing of a second swath, multiple swaths of information can be printed side by side onto a recording medium such that the multiple swaths of information together form a complete printed image.
For optimal print quality, it is important for consecutive swaths of information to be aligned such as to overlap to a precisely defined extent. To that end, each time when a recording medium moves relative to the guiding structure in between the printing of a first swath and the printing of a second swath, the advance of the recording medium can be measured, and compared to an advance as expected based on a prescribed motion of the driving device. The driving device can then be controlled such that the recording medium in a next advancing step advances over a distance larger or smaller than in a previous step, depending on a determined difference between the advance as measured and the advance as expected.
A known method for measuring medium advance in a printer as described comprises the steps of including a first reference mark in a first swath of printed information, including a second reference mark in a second swath of printed information, and optically scanning the two reference marks as printed to determine their relative position on a recording medium along the axis of medium advance, wherein the two reference marks are each printed using a different sub-array of jetting nozzles within the same one nozzle array, the different sub-arrays of jetting nozzles spaced apart within the nozzle array along the axis of medium advance.
The two sub-arrays of jetting nozzles being spaced apart along the axis of medium advance allows the two reference marks to end up printed in the vicinity of each other on a recording medium despite being included in different swaths. This allows both reference marks to reach the field of view of an optical scanner during a specific pass relative to a recording medium of a carriage carrying such a scanner. Given that the relative position of the different sub-arrays of jetting nozzles within the nozzle array is known, the relative position along the axis of medium advance of the two reference marks on a recording medium, as determined with the help of an optical scanner, is indicative of the advance made by the recording medium in between the printing of the first swath and the printing of the second swath.
A known reference mark comprises an array of individually recognizable dot sequences each printed with an individual nozzle of a nozzle array, each dot sequence extending along the axis of carriage motion, the different dot sequences spaced apart along the axis of medium advance. A relative position of two reference marks of this type can be determined by averaging the positions along the axis of medium advance of all dots within a dot sequence; then determining a center of a reference mark along the axis of medium advance based on the average positions of all dot sequences within the reference mark, and then comparing the centers of the two reference marks.
According to a known implementation, in every swath printed, a reference mark assembly can be included, comprising one reference mark printed with a first sub-array of jetting nozzles within a nozzle array, and another reference mark printed with a second sub-array of jetting nozzles within a nozzle array, the two sub-arrays of jetting nozzles spaced apart within the nozzle array along the axis of media advance. Depending on the distance between the two sub-arrays within the nozzle array, after a certain number of swaths printed, the one reference mark as included in a later swath is printed in the vicinity of the other reference mark as included in an earlier swath. This allows the reference marks to be optically scanned in the same one pass of a carriage-mounted optical scanner, such that the relative position along the axis of medium advance of the two reference marks can be determined, and the advance made by a recording medium in between the printing of the earlier swath and the printing of the later swath can be derived.
A reference mark assembly as described is known to be printed in the left and right margins of a print, so that during the printing of an image, the medium advance can be continuously monitored and the motion of a driving device can be repeatedly adjusted if necessary. The width of each reference mark included in the reference mark assembly can be chosen small, depending on the length of a dot sequence required for reliable measurement of a position of each dot sequence along the axis of medium advance. The reference mark assembly is preferably printed in yellow, allowing the reference mark assembly to be virtually invisible to a viewer of a finished print.
The accuracy of a distance determined based on a relative position of two reference marks depends to a large degree on the extent to which the position of each reference mark as printed corresponds with a position of the reference mark as expected. In case a reference mark is printed at a position which is off-set with respect to an expected position, a distance derived from the relative position of two reference marks can be calculated wrong. In the case of medium advance, this may lead to decreased print quality due to inaccurate alignment of consecutive swaths of printed information on a recording medium.
An objective of the present invention is to improve the described method for measuring medium advance in a printer by printing and scanning a pair of reference marks. In particular, the present invention aims to increase the accuracy of the method.

SUMMARY OF THE INVENTION

According to an aspect of the invention, a method for measuring medium advance in a printer by printing and scanning a pair of reference marks as described further comprises the steps of:

printing, in an initial procedure, at least a first initial swath of information and a second initial swath of information;
including in the first initial swath a plurality of first initialization marks each printed with a different array of printing elements;
including in the second initial swath a plurality of second initialization marks each printed with a different array of printing elements;
for each array of printing elements used, determining a relative position of a first initialization mark and a second initialization mark printed with the array, and
determining the medium advance based on the relative position of the two reference marks, taking into account a relation between the relative position of the initialization marks printed with the array of printing elements used for printing the reference marks and the relative position of the initialization marks printed with at least one further array of printing elements.

The invention is based on the insight that a nozzle array used for printing a reference mark is subject to certain imperfections, which may lead to a whole reference mark or a part thereof being printed at an off-set position along the axis of medium advance. This will cause a distance determined based on a relative position of the reference mark and a further reference mark to be calculated wrong. In the case of medium advance, this leads to decreased print quality due to inaccurate alignment of consecutive swaths of printed information on a recording medium.
According to an initial procedure as described, at least a first initial swath of information and a second initial swath of information can be printed, wherein a plurality of first initialization marks each printed with a different nozzle array is included in the first initial swath, and a plurality of second initialization marks each printed with a different nozzle array is included in the second initial swath. For each nozzle array used, a relative position of a first initialization mark and a second initialization mark printed with the array is determined, so that a plurality of values is obtained, each to a certain extent indicative of the advance made by a recording medium in between the printing of the first initial swath and the second initial swath. By determining the medium advance based on the relative position of the two reference marks while taking into account a relation between the relative position of the initialization marks printed with the nozzle array used for printing the reference marks and the relative position of the initialization marks printed with at least one further nozzle array, the medium advance as measured can be corrected for a systemic error caused by an imperfection of a nozzle array having an influence on the positioning of a reference mark, and the medium advance can be more accurately determined.

BRIEF DESCRIPTION OF DRAWINGS

Other objects, features, and advantages of the present invention will become more apparent from the following detailed description when read in conjunction with the accompanying drawings, in which:

Figure 1a shows a schematic perspective view of a scanning-type printer comprising a carriage arranged to move relative to a recording medium along an axis of carriage motion, a guiding structure for guiding the carriage while the carriage is moving, and a roller for driving a recording medium to move relative to the guiding structure along an axis of medium advance normal to the axis of carriage motion;
Figure 1b shows a schematic bottom view of a carriage carrying a plurality of print heads, each print head having a nozzle array, the carriage further carrying an optical scanner;
Figures 2a to 2d schematically show sets of reference marks as included in consecutive swaths of printed information in a known method for measuring medium advance in a printer;
Figures 3 to 6 schematically show sets of initialization marks as included in consecutive swaths of printed information in the initial procedure of a method for measuring medium advance in a printer according to the invention.

DETAILED DESCRIPTION OF EMBODIMENTS

With reference to Figures 1a and 1b, a scanning-type inkjet printer 100 comprises a plurality of inkjet print heads 110, 120, 130, 140 mounted on a print head carriage 150 arranged to move relative to a recording medium 200 along an axis of carriage motion Y while being guided by a guiding structure 160.
The printer 100 comprises a driving roller 170 for driving the recording medium 200 to move relative to the guiding structure 160 along an axis of medium advance X normal to the axis of carriage motion Y.
Each print head 110, 120, 130, 140 has an array 111, 121, 131, 141 of jetting nozzles 180 for jetting out droplets of ink, each nozzle array 111, 121, 131, 141 oriented along the axis of medium advance X.
The carriage 150 carries a scanner 190 having a field of view 191 extending along the axis of medium advance X.
In operation, a swath of information is printed onto the recording medium 200 by jetting nozzles 180 of the print heads 110, 120, 130, 140 ejecting sequences of ink droplets towards the recording medium 200 while the carriage 150 is moving along the axis of carriage motion Y.
In between consecutive swaths, the recording medium 200 is moved along the axis of medium advance X by the driving roller 170, so that multiple swaths of information can be printed side by side on the recording medium 200.
Each time when the recording medium 200 moves relative to the guiding structure 160, the advance of the recording medium 200 is measured, and compared to an advance as expected based on a prescribed motion of the driving roller 170.
For measuring the medium advance, two reference marks printed with different sub-arrays of jetting nozzles 180 within the same one nozzle array 111, 121, 131, 141 are included in each swath of printed information, and a first reference mark and a second reference mark as included in different swaths of printed information are scanned by the scanner 190 to determine their relative position along the axis of medium advance X once the pair of reference marks, by transport of the recording medium 200, has reached an area which is covered by the field of view 191 of the scanner 190 during a certain pass of the carriage 150 relative to the recording medium 200.
With reference to Figures 2a to 2d, in a method for measuring medium advance according to the prior art, in every swath of information S_i printed, a reference mark assembly 50aⁱ, 50bⁱ is included, comprising one reference mark 50aⁱ and another reference mark 50bⁱ.
Each reference mark 50aⁱ, 50bⁱ comprises an array 51a, 51b of individually recognizable dot sequences 53a, 53b each printed with an individual nozzle 180 of the specific nozzle array 111, 121, 131, 141 used for printing the reference mark assembly 50aⁱ, 50bⁱ. Each dot sequence 53a, 53b extends along the axis of carriage motion Y, the different dot sequences 53a, 53b spaced apart along the axis of medium advance X.
The one reference mark 50aⁱ and the other reference mark 50bⁱ are each printed using a different one of two sub-arrays of jetting nozzles 180 spaced apart within the nozzle array 111, 121, 131, 141 used for printing the reference mark assembly 50aⁱ, 50bⁱ, resulting in the reference marks 50aⁱ, 50bⁱ to be printed at a mutual distance dX along the axis of medium advance X.
By appropriate control of the print head 110, 120, 130, 140 comprising the respective nozzle array 111, 121, 131, 141, the reference marks 50aⁱ, 50bⁱ within a certain reference mark assembly 50aⁱ, 50bⁱ furthermore are printed at a mutual distance dY along the axis of carriage motion Y.
As a result of the distances dX, dY between the reference marks 50aⁱ, 50bⁱ within a certain reference mark assembly 50aⁱ, 50bⁱ, and as illustrated by the reference mark assemblies 50a¹, 50b¹; 50a², 50b²; 50a³, 50b³; 50a⁴, 50b⁴ included in consecutive swaths of printed information S₁ to S₄ shown in Figures 2a to 2d, after a certain number of swaths printed (four, in the shown example), the one reference mark 50a⁴ as included in a later swath S₄ is printed in the vicinity of the other reference mark 50b¹ as included in an earlier swath S₁ (see Figure 2d). This allows the two reference marks 50a⁴, 50b¹ to be scanned by the scanner 190 in the same one pass of the carriage 150 relative to the recording medium 200, such that the relative position along the axis of medium advance X of the two reference marks 50a⁴, 50b¹ can be determined, and the advance made by the medium 200 in between the printing of the earlier swath S₁ and the printing of the later swath S₄ can be derived.
With reference to Figures 3 to 6, in the initial procedure of a method for measuring medium advance according to the invention, a plurality of initial swaths of information I₁, I₂, I₃, I₄ is printed, wherein the recording medium 200 is moved over a certain distance along the axis of medium advance X in between the printing of consecutive swaths I₁, I₂, I₃, I₄.
In every initial swath I_i printed, a plurality of initialization mark assemblies 10aⁱ, 10bⁱ; 20aⁱ, 20bⁱ; 30aⁱ, 30bⁱ; 40aⁱ, 40bⁱ is included, printed at different positions along the axis Y of carriage motion. At least some of the initialization mark assemblies 10aⁱ, 10bⁱ; 20aⁱ, 20bⁱ; 30aⁱ, 30bⁱ; 40aⁱ, 40bⁱ included in each swath I_i are printed with different nozzle arrays 111, 121, 131, 141, as indicated in Figures 3 to 6 by the different line types used for the dot sequences 63a, 63b of the various initialization mark assemblies 10aⁱ, 10bⁱ; 20aⁱ, 20bⁱ; 30aⁱ, 30bⁱ; 40aⁱ, 40bⁱ shown (solid, dotted, short dash, long dash).
In the shown embodiment, groups of multiple initialization mark assemblies 10aⁱ, 10bⁱ; 20aⁱ, 20bⁱ; 30aⁱ, 30bⁱ; 40aⁱ, 40bⁱ each printed with the same one nozzle array 111, 121, 131, 141 are included in each initial swath I_i, the different initialization mark assemblies 10aⁱ, 10bⁱ; 20aⁱ, 20bⁱ; 30aⁱ, 30bⁱ; 40aⁱ, 40bⁱ within each group printed at different positions along the axis of carriage motion Y.
Each initialization mark assembly 10aⁱ, 10bⁱ; 20aⁱ, 20bⁱ; 30aⁱ, 30bⁱ; 40aⁱ, 40bⁱ comprises a primary initialization mark 10aⁱ, 20aⁱ, 30aⁱ, 40aⁱ and a secondary initialization mark 10bⁱ, 20bⁱ, 30bⁱ, 40bⁱ, each printed with a different sub-array of jetting nozzles 180 of the nozzle array 111, 121, 131, 141 used for printing the initialization mark assembly 10a', 10b'; 20aⁱ, 20bⁱ; 30aⁱ, 30bⁱ; 40aⁱ, 40bⁱ.
Like a reference mark 50aⁱ, 50bⁱ as described, each initialization mark 10aⁱ, 10bⁱ, 20aⁱ, 20bⁱ, 30aⁱ, 30bⁱ, 40aⁱ, 40bⁱ, comprises an array 61a, 61b of individually recognizable dot sequences 63a, 63b each printed with an individual nozzle 180 of the specific nozzle array 111, 121, 131, 141 used for printing the respective initialization mark assembly 10aⁱ, 10bⁱ; 20aⁱ, 20bⁱ; 30aⁱ, 30bⁱ; 40aⁱ, 40bⁱ, each dot sequence 63a, 63b again extending along the axis of carriage motion Y, the different dot sequences 63a, 63b spaced apart along the axis of medium advance X.
Like in a reference mark assembly 50aⁱ, 50bⁱ as described, the two initialization marks 10aⁱ, 10bⁱ; 20aⁱ, 20bⁱ; 30aⁱ, 30bⁱ; 40aⁱ, 40bⁱ are each printed using a different one of two sub-arrays of jetting nozzles 180 spaced apart within the nozzle array 111, 121, 131, 141 used for printing the initialization mark assembly 10aⁱ, 10bⁱ; 20aⁱ, 20bⁱ; 30aⁱ, 30bⁱ; 40aⁱ, 40bⁱ, resulting in the initialization marks 10aⁱ, 10bⁱ; 20aⁱ, 20bⁱ; 30aⁱ, 30bⁱ; 40aⁱ, 40bⁱ to be printed at a mutual distance dX along the axis of medium advance X.
The two initialization marks 10aⁱ, 10bⁱ; 20aⁱ, 20b'; 30aⁱ, 30bⁱ; 40aⁱ, 40bⁱ are furthermore printed at a mutual distance dY along the axis of carriage motion Y.
Each initialization mark assembly 10aⁱ, 10bⁱ; 20aⁱ, 20bⁱ; 30aⁱ, 30bⁱ; 40aⁱ, 40bⁱ, like a reference mark assembly 50aⁱ, 50bⁱ, serves as a means for measuring the advance of the recording medium 200 in between the printing of consecutive swaths I₁, I₂, I₃, I₄.
As a result of the distances dX, dY between the initialization marks 10aⁱ, 10bⁱ; 20aⁱ, 20bⁱ; 30aⁱ, 30bⁱ; 40aⁱ, 40bⁱ within a certain initialization mark assembly 10aⁱ, 10bⁱ; 20aⁱ, 20bⁱ; 30aⁱ, 30bⁱ; 40aⁱ, 40bⁱ, and as illustrated by Figures 3 to 6, after a certain number of initial swaths printed (four, in the shown example), a primary initialization mark 10a⁴, 20a⁴, 30a⁴, 40a⁴ printed with a certain nozzle array 111, 121, 131, 141 as included in a later swath I₄ is printed in the vicinity a secondary initialization mark 10b¹, 20b¹, 30b¹, 40b¹ printed with the same one nozzle array 111, 121, 131, 141 as included in an earlier swath I₁ (see Figure 6). This allows the two initialization marks 10a⁴, 10b¹; 20a⁴, 20b¹; 30a⁴, 30b¹; 40a⁴, 40b¹ to be scanned by the scanner 190 of the printer 100 in the same one pass of the carriage 150 relative to the recording medium 200, such that the relative position along the axis of medium advance X of the two initialization marks 10a⁴, 10b¹; 20a⁴, 20b¹; 30a⁴, 30b¹; 40a⁴, 40b¹ can be determined.
With the different initialization mark assemblies 10aⁱ, 10bⁱ; 20aⁱ, 20bⁱ; 30aⁱ, 30bⁱ; 40aⁱ, 40bⁱ printed at different positions along the axis of carriage motion Y, the relative position of each pair of initialization marks 10a⁴, 10b¹; 20a⁴, 20b¹; 30a⁴, 30b¹; 40a⁴, 40b¹ printed in the vicinity of each other is indicative of the advance made by the recording medium 200 in between the printing of the earlier swath I₁ and the printing of the later swath I₄.
Based on a relation between the relative position of the initialization marks 10b¹, 10a⁴ printed with a nozzle array 111 that will later be used for printing reference marks 50aⁱ, 50bⁱ and the relative position of the initialization marks 20b¹, 20a⁴; 30b¹, 30a⁴; 40b¹, 40a⁴ printed with at least one further nozzle array 121, 131, 141, the accuracy of a procedure for measuring medium advance performed after the initial procedure can be improved.
According to a relatively simple embodiment, for each pair of initialization marks 10b¹, 10a⁴; 20b¹, 20a⁴; 30b¹, 30a⁴; 40b¹, 40a⁴ scanned, the relative position of the two marks 10b¹, 10a⁴; 20b¹, 20a⁴; 30b¹, 30a⁴; 40b¹, 40a⁴ is determined, and an amount of medium advance is derived based on the determined relative position and the distance between the different sub-arrays of jetting nozzles 180 used for printing the two marks 10b¹, 10a⁴; 20b¹, 20a⁴; 30b¹, 30a⁴; 40b¹, 40a⁴.
Based on the amount of medium advance determined for each pair of reference marks 10b¹, 10a⁴; 20b¹, 20a⁴; 30b¹, 30a⁴; 40b¹, 40a⁴, an average amount of medium advance can be calculated, and the difference between the average amount and the advance determined based on the relative position of the initialization marks 10b¹, 10a⁴ printed with a nozzle array 111 to be used for printing a pair of reference marks 50a⁴, 50b¹ in a procedure for measuring the medium advance can be determined.
A difference as described can be seen as a systemic error in a method for measuring medium advance according to the prior art, caused by an imperfection of the one nozzle array 111 used for printing the pair of reference marks 50a⁴, 50b¹ scanned in the method. By correcting for the difference after determining an amount of medium advance based on a relative position of the pair of reference marks 50a⁴, 50b¹, in a procedure for measuring the medium advance following the initial procedure, the measuring error is at least reduced, and the medium advance can be determined relatively accurately.
It is noted that the accuracy is further increased by having groups of multiple initialization mark assemblies 10aⁱ, 10bⁱ; 20aⁱ, 20bⁱ; 30aⁱ, 30bⁱ; 40aⁱ, 40bⁱ each printed with the same one nozzle array 111, 121, 131, 141 included in each initial swath I_i, so that a more accurate average of medium advance can be obtained.
Further improvement is obtained when initialization mark assemblies 10aⁱ, 10bⁱ; 20aⁱ, 20bⁱ; 30aⁱ, 30bⁱ; 40aⁱ, 40bⁱ printed with the same one nozzle array 111, 121, 131, 141 are included in consecutive initial swaths I_i at different positions along the axis of carriage motion Y, to decrease the influence of any Y-position-related error in the X-position of an initialization mark 10aⁱ, 10bⁱ, 20aⁱ, 20bⁱ, 30aⁱ, 30bⁱ, 40aⁱ, 40bⁱ, caused by any imperfection of the guiding structure 160 influencing the motion of the carriage 150.
A relative position of two initialization marks 10a⁴, 10b¹; 20a⁴, 20b¹; 30a⁴, 30b¹; 40a⁴, 40b¹ along the axis of medium advance X can be determined by averaging the positions along the axis of medium advance X of all dots within a dot sequence 63a, 63b; then determining a center of an initialization mark 10a⁴, 10b¹; 20a⁴, 20b¹; 30a⁴, 30b¹; 40a⁴, 40b¹ along the axis of medium advance X based on the average positions of all dot sequences 63a, 63b within the initialization mark 10a⁴, 10b¹; 20a⁴, 20b¹; 30a⁴, 30b¹; 40a⁴, 40b¹, and then comparing the centers of the two initialization marks 10a⁴, 10b¹; 20a⁴, 20b¹; 30a⁴, 30b¹; 40a⁴, 40b¹.
For sake of completeness, it is noted that an initialization mark 10aⁱ, 10bⁱ, 20aⁱ, 20bⁱ, 30aⁱ, 30bⁱ, 40aⁱ, 40bⁱ printed at a certain position along a certain axis X, Y is centered about that certain position along said certain axis X, Y.
It is to be understood that the disclosed embodiments are merely exemplary of the invention, which can be embodied in various forms. Specific structural and functional details are not to be interpreted as limiting, but merely as a basis for the claims and as a teaching for one skilled in the art to variously employ the present invention in virtually any appropriately detailed structure. In particular, features presented and described in separate dependent claims may be applied in combination, and any advantageous combination of such claims is herewith disclosed.
The invention being thus described, it will be obvious that the same may be varied in many ways. Such variations are not to be regarded as a departure from the spirit and scope of the invention, and all such modifications as would be obvious to one skilled in the art are intended to be included within the scope of the following claims.

Claims

Method for measuring medium advance in a printer (100) comprising one or more print heads (110, 120, 130, 140) mounted on a carriage (150) arranged to move relative to a recording medium (200) along an axis of carriage motion (Y), the one or more print heads (110, 120, 130, 140) together having at least two arrays (111, 121, 131, 141) of printing elements (180), wherein a swath of information (S₁, S₂, S₃, S₄) can be printed onto a recording medium (200) by an array (111, 121, 131, 141) of printing elements (180) of a print head (110, 120, 130, 140) printing information onto the recording medium (200) while the carriage (150) is moving, the method comprising the steps of:
- including in a first swath of printed information (S₁) a first reference mark (50b¹) printed with one array (111) of printing elements (180);

- including in a second swath of printed information (S₄) a second reference mark (50a⁴) printed with the one array (111) of printing elements (180), and

- determining a relative position of the two reference marks (50b¹, 50a⁴), the method further comprising the steps of:

- printing, in an initial procedure, at least a first initial swath of information (I₁) and a second initial swath of information (I₄);

- including in the first initial swath (I₁) a plurality of first initialization marks (10b¹, 20b¹, 30b¹, 40b¹) each printed with a different array (111, 121, 131, 141) of printing elements (180);

- including in the second initial swath (I₄) a plurality of second initialization marks (10a⁴, 20a⁴, 30a⁴, 40a⁴) each printed with a different array (111, 121, 131, 141) of printing elements (180);

- for each array (111, 121, 131, 141) of printing elements (180) used, determining a relative position of a first initialization mark (10b¹, 20b¹, 30b¹, 40b¹) and a second initialization mark (10a⁴, 20a⁴, 30a⁴, 40a⁴) printed with the array (111, 121, 131, 141), and

- determining the medium advance based on the relative position of the two reference marks (50b¹, 50a⁴), taking into account a relation between the relative position of the initialization marks (10b¹, 10a⁴) printed with the one array (111) of printing elements (180) and the relative position of the initialization marks (20b¹, 20a⁴; 30b¹, 30a⁴; 40b¹, 40a⁴) printed with at least one further array (121, 131, 141) of printing elements (180).
Method according to claim 1, wherein multiple sets of a first initialization mark (10aⁱ, 20aⁱ, 30aⁱ, 40aⁱ) and a second initialization mark (10bⁱ, 20aⁱ, 30aⁱ, 40aⁱ) printed with the same one array (111, 121, 131, 141) of printing elements (180) are included in each initial swath (I_i) at different positions along the axis of carriage motion (Y).
Method according to claim 1 or 2, wherein sets of a first initialization mark (10aⁱ, 20aⁱ, 30aⁱ, 40aⁱ) and a second initialization mark (10bⁱ, 20aⁱ, 30aⁱ, 40aⁱ) printed with the same one array (111, 121, 131, 141) of printing elements (180) are included in consecutive initial swaths (I_i) at different positions along the axis of carriage motion (Y).
Method according to one of the preceding claims, wherein an amount of medium advance as determined based on the relative position of the pair of reference marks (50b¹, 50a⁴) is corrected based on a difference between an average amount of medium advance determined based on the relative positions of the various pairs of initialization marks (10b¹, 10a⁴; 20b¹, 20a⁴; 30b¹, 30a⁴; 40b¹, 40a⁴) and an amount of medium advance determined based on the relative position of the initialization marks (10b¹, 10a⁴) printed with the one array (111) of printing elements (180).