Process control of electrophotographic device

A method is described to control the maximum density and the pixel profile of microdots produced by a binary or multilevel electrophotographic device. In various embodiments, from the maximum development potential. The working point of the device is established by imposing a relation between charge level, discharge level and saturation voltage level of the photosensitive element. This allows to achieve consistent output densities, irrespective of the environmental parameters, such as relative humidity and temperature.

FIELD OF THE INVENTION 
The present invention relates to devices and methods for hardcopy printing. 
More specifically the invention is related to a hardcopy device that has 
an exposure subsystem that is responsible for the generation of a latent 
image on a photosensitive medium. This medium may be the final image 
carrier after development or alternatively an intermediate member, where 
the latent images are developed using developers of the appropriate 
colours and where the developed sub-images are transferred to the final 
substrate as is the case in electrophotography. 
More specifically, the present invention relates to devices and methods for 
an image forming apparatus, such as an electrophotographic digital copying 
machine or digital printer with a two-component development system. 
BACKGROUND OF THE INVENTION 
Various electronic devices are available on the market that transform a 
digital or electronic image to appropriate density variations on an image 
carrier, in order to render the electronic image visible on the image 
carrier. Alternatively, the electronic image is converted to an image-wise 
distribution of ink repellant and ink accepting zones on a printing plate, 
for use in e.g. offset printing. 
An electronic image is typically represented by a rectangular matrix of 
pixels, each having a pixel value. The location of each pixel within the 
matrix corresponds to a specific location on the image carrier. Each pixel 
value corresponds to an optical density required on the image carrier at 
the specific location. 
In a binary system, two pixel values, e.g. 0 and 1, are sufficient, to 
represent a high density and a low density, which may be obtained by 
applying ink and no ink respectively, or toner and no toner, or generating 
locally dye or no dye, or by keeping and removing silver in a photographic 
process. In the production of printing plates, 0 may result in an ink 
repellant zone, where 1 results in an ink accepting zone. 
In a continuous tone system, multiple density levels may be generated on 
the image carrier, with no perceptible quantisation to them. In order to 
achieve such fine quantisation, usually 256 different density levels are 
required, such that each pixel value may range from 0 to 255. In 
electrophotography usually a reduced number of density levels can be 
generated consistently, e.g. 16 levels, in which case the system is called 
a multilevel system, as opposed to a binary system or a continuous tone 
system. 
As said before, each "zone" or "microdot" on the image carrier gets a 
density, corresponding to a pixel value from the electronic image. Such 
zone is further on indicated by the term "microdot". A microdot is the 
smallest space on the image carrier that can get an optical density (or 
ink repellency) different from neighbouring locations. Usually microdots 
are represented by squares or rectangles within parallel and orthogonal 
grid lines. The spacing of the grid lines is indicative for the resolution 
of the output device. 
For each microdot on the image carrier, one pixel value is required. In an 
output device, based on image generation by exposure to light, the 
microdots are usually illuminated sequentially one at a time by (one or 
more) scanning laser beams. Microdots may be illuminated one row at a 
time, as with emitting LED bars or through spatial light modulators like 
liquid crystal (LCD) shutters or digital mirror devices (DMD). 
A typical laser scanner example is the Agfa P3400 laser printer, marketed 
by Agfa-Gevaert N. V., which is a 400 dpi (dots per inch, one inch is 25.4 
mm) printer. Each microdot has approximately a size of 62 .mu.m. The 
diameter of the circular spot is typically 88 .mu.m. This means that 
within a radius of 44 .mu.m the illuminance (W/m.sup.2) of the light beam 
is everywhere higher than 50% of the maximum illuminance. The illumination 
is usually nearly Gaussian distributed. This means that the illuminance is 
maximal in the centre of the microdot or in the centre of the circular 
spot, and decays as the distance from this centre increases. In some 
systems, an elliptical spot is preferred above a circular spot. Usually, 
the short axis of the ellipse is oriented along the fast scan direction of 
the laser beam, to compensate for the elongation of the illumination spot 
as the beam moves during the finite exposure times. 
A typical LED exposure example is the Agfa P400 laser printer, marketed by 
Agfa-Gevaert N. V., which is equally a 400 dpi (dots per inch) printer and 
has an extension of the spot of typically 88 .mu.m. 
In an electrophotographic system, multilevel exposure at the microdot level 
is used to reduce tone gradation coarseness at a given screen ruling 
associated with the limited addressability. Exposure intensity at the 
pixel level is varied and the operation point on the discharge curve is 
chosen such as to have a nearly linear discharge behaviour as a function 
of exposure for most of the exposure range used. 
Because of the smooth gradation response of the photosensitive medium, for 
which preferentially the conductivity varies when photons impinge on its 
surface, e.g. an organic photoconductor (OPC), an essentially uniform 
energy distribution within the microdot is required. Moreover, a suitable 
working point of the electrophotographic process is required. This working 
point is characterised by parameters which are discussed in detail below. 
One of the main factors to quantify the quality of a printed image is the 
tone scale representation, expressed by the optical density range and the 
exactness and stability of the contone rendering. In a digital printing 
machine, such as an electrophotographic engine, each tone of a contone 
image is produced by a certain spatial combination of some or all of the 
available tones per pixel. This process is referred to as screening. The 
set of tones, available in the machine, is defined by the properties of 
the exposure device. For instance, in an electrophotographic printer that 
uses a binary exposure device, only two tones (black and white) are 
available to the screening algorithm to reproduce a contone image. In some 
machines however, multiple tone levels are available to the screening 
process by applying area or intensity modulation on the output spot of the 
exposure device (see below). As screening is well-defined and, by its 
nature, perfectly repeatable, the image quality of the engine is largely 
determined by the ability to reproduce the set of tones. In an 
electrophotographic engine the contone density of each microdot is 
determined by the mass of toner per unit area transferred to paper. This 
toner mass, referred to as M/A and expressed in mg/cm.sup.2, is a function 
of an almost limitless amount of parameters. Most of these parameters can 
be regarded as fixed by design and thus invariable during the operation of 
the engine. Some however are extremely variable. The most important in a 
two-component developer system are: 
toner concentration (TC)=the ratio of the amount of toner and the amount of 
carrier available in the developing unit in a two-component system. 
toner charge per unit of mass (Q/M), expressed in .mu.C/g. development 
potential (V.sub.DEV), expressed in Volt=the potential difference V.sub.E 
-V.sub.B over the development gap between the developer supply roller 
(bias voltage V.sub.B) and the photosensitive element (voltage after 
exposure V.sub.E) upon which a latent image is present. The photosensitive 
element is mostly implemented as an Organic Photoconductor or OPC. 
transfer efficiency (TE), expressed in %: the ratio of the amount of toner 
transferred to the printing medium and the amount of toner developed on 
the photosensitive element. This dependency can be formally expressed as: 
EQU M/A=f (TC, Q/M, V.sub.DEV, TE ) 
and is generally referred to as the develop ability and transferability of 
the toner. 
In an electrophotographic engine, the reproduction of multiple tones is 
highly sensitive to each of these variables. Toner concentration TC 
changes during engine operation due to depletion of toner caused by image 
development and toner addition under control of the engine. Toner charge 
Q/M is determined by: 
the triboelectric properties of toner and carrier, 
toner concentration TC, 
relative humidity RH of the air in the developing unit, 
agitation of developer in the developing unit. 
When the developer is properly agitated, an unambiguous relationship can be 
found between Q/M, TC and RH. The development potential V.sub.DEV is 
determined by: 
the initial charge level V.sub.C of the OPC, 
the bias voltage V.sub.B applied to the toner supply roller of the 
developing unit and 
the intensity E.sub.EXP of the image dependent illumination of the 
photosensitive element. 
Transfer efficiency TE on its turn is, amongst other factors, determined 
by: 
toner charge Q/M, 
amount of toner on the photosensitive element and 
the value of the electric field in the transfer zone. 
Present electrophotographic machines maintain the optical density of their 
produced tones by keeping toner concentration TC at a constant level. For 
this purpose they use a toner concentration sensor in the developing unit, 
or a density sensor that measures the density D.sub.OPC developed on the 
OPC, or both. Changes of the toner charge Q/M, due to relative humidity RH 
or variations of RH are compensated for by changing the development 
potential V.sub.DEV and the value of the transfer electric field. 
Disadvantages of this technique are: 
extremely low toner charge Q/M at high relative humidity RH, leading to an 
increase in dust production, fogging and possibly inconsistent transfer 
quality over the whole tone scale. 
extremely high toner charge at low relative humidity, decreasing the 
develop ability of the toner. This requires large electric fields in the 
developing stage and consequently implies more powerful engine hardware. 
Furthermore, it can be shown that for a two-component developing system, 
the development of the latent image is almost purely driven by toner 
charge Q/M. Therefore toner charge Q/M would be a valuable input to any 
process control system for steering the electrophotographic process. 
Generally, online toner charge measurement Q/M can not be implemented 
easily without the need for high precision measurement hardware, which 
leads to an increase in system variable cost. As stated before, producing 
several tones in an electrophotographic engine can be done by area 
modulation or by intensity modulation of the light beam of the exposure 
device (or by any combination of both). In this way, a set of microscopic 
tones at the pixel or microdot level are created. These form a microscopic 
gradation that has to be kept constant for the contone rendering, handled 
by the screening process, to be repeatable. The relation between the 
modulated output E.sub.EXP of the exposure device and the resulting 
development potential V.sub.DEV is extremely non-linear. Worse due to the 
necessary cleaning potential V.sub.CL (difference between charge potential 
V.sub.C and bias potential V.sub.B), there is always a range in the 
exposure intensity E.sub.EXP where no development potential V.sub.DEV is 
created. The exposure energy E.sub.EXP has to exceed a certain threshold 
before any development occurs. As explained above, due to changes in the 
develop ability of the developer (Relative Humidity RH, developer age, 
etc.), the development potential V.sub.DEV has to be changed in order to 
maintain the proper image density D. This implies changing the charge 
potential V.sub.C and the bias potential. By doing this, the relationship 
between output energy E.sub.EXP of the exposure device and the resulting 
development potential V.sub.DEV is altered, causing a dramatic change on 
the microscopic gradation D. The modulation function, used for converting 
tone levels I of the original image to exposure energy E.sub.EXP levels 
has to be redefined. In present electrophotographic machines a global 
linear shift and/or resealing is applied to the exposure modulation 
function (I, E.sub.EXP), see for instance U.S. Pat. No. 5,305,057. Because 
of the non-linearity and the threshold phenomenon described above, this is 
clearly not enough in order to maintain the highest possible contone 
fidelity. There is still another effect that one has to consider when 
producing images in a digital electrophotographic engine. Present 
electrophotographic engines maintain the discharge potential V.sub.E or 
the potential of the OPC after exposure at maximum exposure (=maximum 
density) at one predefined level. Changes in develop ability will require 
other development potentials V.sub.DEV and thus other charge potentials 
V.sub.C. Keeping the discharge level (E.sub.EXP).sub.MAX at the same point 
will consequently put the point of maximum exposure at a different point 
of the sensitometric curve of the OPC. The non-linear behaviour of this 
sensitometric curve will cause the shape of individual pixels to change 
dramatically due to the saturation effect. This changes individual pixel 
sizes and the contone rendering created by the screening process. FIG. 11 
and FIG. 12 illustrate the above described effects. FIG. 11 shows two 
discharge curves for a typical OPC: one curve 50 for a high charge voltage 
V.sub.C =-440 V needed at low humidity, RH=30%, the second curve 51 for a 
lower charge voltage V.sub.C =-330 V needed at high humidity, RH=70%. The 
horizontal line 52 indicates the constant discharge potential 
(V.sub.E).sub.MAX for maximum exposure. On the horizontal E.sub.EXP -axis, 
the corresponding maximum exposure energy level E.sub.MAX for the 
respective humidity levels RH are found. FIG. 12 shows the resulting pixel 
profiles in deposited mass M/A in mg/cm.sup.2 for an exposure device with 
a typical gaussian spot. The maximum intensity or energy level of the spot 
is given by the respective E.sub.MAX values from FIG. 11. The graph 53 
shows the pixel profile that corresponds with a low relative humidity 
RH=30%. The graph 54 shows the pixel profile that corresponds with a high 
relative humidity RH=70%. From the graph it is clear that the change in 
pixel size is not negligible. 
OBJECTS OF THE INVENTION 
It is therefore a first object of the invention to provide methods and 
devices for halftone image printing with improved tone scale linearity for 
electrophotographic systems, wherein a required density is achieved. 
It is yet another object of the invention to provide a method for defining 
the operating point of the engine in such a way that the contone rendering 
made available through the screening process is kept stable and 
repeatable. 
Further objects of the invention will become apparent from the description 
hereinafter. 
SUMMARY OF THE INVENTION 
The above mentioned objects are realised by the specific features according 
to claim 1. Specific features for preferred embodiments of the invention 
are set out in the dependent claims. 
These objects can be accomplished according to the present invention by an 
electrophotographic image forming apparatus as shown in FIG. 1. This 
apparatus comprises a charging device 2, such as a scorotron, that charges 
a photosensitive element 1, such as an Organic Photo conductor (OPC). The 
charged photoconductor 1 is exposed by an exposure device 3. such as a 
LASER, an LED-array, a spatial light modulator (like a DMD: deflective 
mirror device) etc., to form a latent image. The latent image is developed 
by a two-component developing system to form a toner image. The toner 
image is transferred to an output medium 22 such as paper or transparency 
and fused by applying heat and/or mechanical pressure. The apparatus 
preferentially comprises a densitometer 6 that measures the optical 
density D of the image developed on the OPC, preferably to correct the 
developing process for possible deviations. The apparatus preferably 
contains a contact-less electrostatic voltage sensor 4 that measures the 
surface potential of the OPC 1. The apparatus preferably also contains a 
toner concentration sensor 16, preferentially located in the developing 
system 5. The developability and transferability of the toner particles 
are maintained over the complete range of environmental conditions, 
developer lifetime, etc. by keeping the charge of the toner, Q/M, within a 
narrow range. This range is defined by the unambiguous relationship 
between Q/M, TC and RH and the range for TC that can be allowed without 
penalizing developer lifetime. By changing the toner concentration TC by 
means of toner addition or toner depletion during operation of the engine, 
toner charge Q/M can be maintained at its required level. Toner charge Q/M 
may be indirectly measured, based upon the unambiguous relationship that 
exists between M/A, Q/M and V.sub.DEV, for that range of M/A where 
development is not limited by toner supply (low- and midtones). The 
operating point of the engine (charge level V.sub.C, exposure intensity 
E.sub.MAX at maximum density, cleaning potential V.sub.CL) is calculated 
in such a way that possible line width increase is taken into account. 
Proper microscopic gradation D.sub.i is maintained by re-positioning each 
exposure level E.sub.EXP, relating to a microscopic tone, along the 
complete range of available output energy levels E.sub.EXP, every time the 
D.sub.i operating point of the engine is changed. 
Further advantages and embodiments of the present invention will become 
apparent from the following description and drawings.

DETAILED DESCRIPTION OF THE INVENTION 
Electrophotographic engine 
The most important components of an electrophotographic imaging apparatus 
suitable for the current invention are shown in FIG. 1. A photosensitive 
element 1, such as an OPC, is charged by a charging device 2 (such as a 
scorotron) and exposed by an exposure device 3 (laser scan system, 
LED-array, DMD, etc.). The exposure device 3 is capable of generating more 
than one exposure energy level E.sub.EXP per pixel. For instance a binary 
device can image two levels (0 and some other level different from 0), a 
16-level (4 bit/pixel information) exposure device can generate 16 
distinguishable levels per pixel (including 0), etc. The exposure device 3 
receives image data 33 from an image processing unit 14, generally called 
a RIP or Raster Image Processor, which translates image data, presented in 
a page description language, to a bitmap. The bitmap contains the required 
exposure tone level I for each pixel in the image. Inside the exposure 
device 3 there is preferably a translation table 15 (look-up-table or LUT) 
to translate the data in the bitmap to physical exposure energy levels 
E.sub.EXP. The effect of charging to a charge voltage V.sub.C and 
subsequently discharging by exposure E.sub.EXP can be measured by a 
contact-less electrostatic voltage sensor 4. The resultant latent image is 
developed by a two-component developing system 5. Charged toner particles 
are transferred from the magnetic brush 8 to the OPC surface by the force 
of the electric field V.sub.DEV present between the OPC surface at 
potential V.sub.E and the surface of the magnetic roller at potential 
V.sub.B. The density D.sub.OPC 31 of the developed image can be measured 
with a densitometer 6 focused on the OPC surface. The engine comprises a 
toner container 12 from which toner can be added to the developing unit 5 
through a control means 13. The developing unit 5 further preferably 
contains a toner concentration sensor 16 which is merely used as a 
watchdog for detecting extreme toner concentration values. The toner image 
is transferred to a medium 7 (paper, transparency, etc.). The engine also 
contains an environmental sensor 9 (referred to as RH/T sensor) that 
senses both relative humidity RH and temperature T. Toner particles that 
are not transferred to the medium 7 are scraped from the OPC by a cleaner 
system 11 and dumped into the toner waste box 10. 
In order to facilitate the concepts to follow, a definition of potentials, 
voltages and terms is given, in conjunction with FIG. 1 and FIG. 2. All 
potentials are referred to the ground potential of the OPC (1). 
V.sub.C charge potential (33): potential to which the OPC is brought by the 
charge station (2). In the example of FIG. 2, V.sub.C has a value of -425 
Volt. 
V.sub.e potential (27) after exposure E (expressed in mJ/m.sup.2) of the 
OPC. 
V.sub.E potential after maximal exposure E.sub.MAX of the OPC. The exposure 
E by a light source, such as a lamp or an LED, which impinges on the OPC, 
may be expressed in mJ/m.sup.2. Maximal exposure E=E.sub.MAX of two 
neighbouring microdots may influence this potential V.sub.E after maximal 
exposure. A typical value for V.sub.E is -125 V. whereas a typical value 
for E.sub.MAX is 3 mJ/m.sup.2. 
V.sub.B bias voltage (29) between 
the developer subsystem (5) supplying the toner; and, 
the ground potential of the OPC (1). 
A typical value for V.sub.B is -325 V, as shown in FIG. 2. 
V.sub.DEV development potential=V.sub.E -V.sub.B. A typical voltage to 
achieve full development to solid toner is 325-125=200 V. 
V.sub.CL cleaning potential=V.sub.B -V.sub.C. A typical value for repelling 
enough toner particles from a non-exposed area is 425-325=100 V. V.sub.CL 
is usually between 50 and 100 V 
V.sub.SAT saturation potential. This potential is shown on FIG. 2 and is 
defined by the asymptotic value for E.fwdarw..ltoreq. for the curve in 
FIG. 2, as indicated by the arrow. 
Charge voltage V.sub.C and discharge voltage V.sub.e can be measured using 
a contact-less electrostatic voltmeter such as a TREK model number 856 
(trademark of TREK Inc.), which is preferentially mounted towards the OPC 
surface. 
The approach followed, to define the process parameters for the reversal 
development process, is described by reference to FIG. 2. In abscissa, the 
exposure energy level E is shown, expressed in mJ/m.sup.2. In ordinate, 
the potential after exposure V.sub.e is shown, expressed in Volt and with 
reference to the saturation voltage V.sub.SAT, the bias voltage V.sub.B 
and the charge potential V.sub.C. The curve in FIG. 2 shows the discharge 
curve, which gives the potential V.sub.e on the OPC after exposure by an 
energy E. In normal operation, the exposure system is operated between 0 
and E.sub.MAX, such that the potential V.sub.e may vary between V.sub.C 
and V.sub.E. 
The process parameters shown in FIG. 2 are preferentially obtained in the 
following way. The saturation voltage V.sub.SAT, or saturation exposure 
potential, is a system parameter, determined mainly by the OPC type, the 
processing speed, the engine geometry (clock position of charging (2) and 
development (5)) and erase lamp settings (fatigue). Once the building 
components of the system are defined, V.sub.SAT is fixed. A typical value 
for V.sub.SAT is -50 V. 
Next V.sub.CL is determined for a given development system. The value for 
the cleaning potential V.sub.CL must be selected such that the fog level 
of the printing system is visually acceptable. If V.sub.CL is too low, 
then locations on the OPC having a voltage level of V.sub.C would not 
repel toner particles, resulting in fog on the printed document. On the 
other hand, selecting V.sub.CL too high gives other problems. A typical 
value for V.sub.CL is 100 V. 
According to FIG. 2, two parameters may be further fixed: i.e. V.sub.DEV 
and V.sub.C. By changing V.sub.C, the shape of the curve as shown in FIG. 
2 is changed. If V.sub.C is increased to a higher voltage, then the whole 
curve moves to a higher position, since its asymptotic value V.sub.SAT 
remains the same. If V.sub.C is decreased, the discharge curve moves to a 
lower position. In a first preferred embodiment, V.sub.C and V.sub.DEV 
must be selected such that the following two conditions are satisfied: 
A. the required density D.sub.MAX or target full solid density development, 
being a design specification e.g. D.sub.MAX =1.8 for black toner, is 
obtained on the printed material by exposure E.sub.MAX, giving exposure 
voltage V.sub.E ; and, 
B. V.sub.E =V.sub.SAT -1/4 (V.sub.DEV +V.sub.CL) 
Values satisfying these two conditions may be found by an iterative 
procedure, which may go as follows. First a reasonable value for V.sub.C 
is selected, say V.sub.C1. By subsequent exposure of the OPC, pre-charged 
at V.sub.C1, by different exposure levels E.sub.J. different values for 
V.sub.e, i.e. V.sub.e1J are obtained. The exposure voltage V.sub.e1J 
depends not only on the exposure level E.sub.J, but also on the charge 
potential V.sub.c1, hence the index 1. By plotting V.sub.e1J as a function 
of E.sub.J, a curve as shown in FIG. 2 is obtained. The system having 
charge potential V.sub.C1 is now used to produce printed output. A 
suitable value for E.sub.MAX is selected, in order to produce a toner 
image. The optical density D of the toner image is measured and compared 
to D.sub.MAX, the required highest density. If D is lower than D.sub.MAX, 
then E.sub.MAX is increased, if D is higher than D.sub.MAX, then E.sub.MAX 
is decreased, until a value for E.sub.MAX is found, suitable for producing 
the density D.sub.MAX. From the curve in FIG. 2, given the suitable 
exposure level E.sub.MAX, the corresponding value V.sub.E can be obtained. 
Alternatively, this value V.sub.E may be measured during printing printing 
D.sub.MAX. Since V.sub.C1 and V.sub.CL are fixed, V.sub.DEV may be 
computed. This value V.sub.DEV is used to assess the equation: V.sub.E 
=V.sub.SAT -1/4 (V.sub.DEV +V.sub.CL) if this is approximately fulfilled, 
e.g. within 10% or preferably 5%, then the iteration stops and good values 
for both V.sub.C and V.sub.DEV have been found. Otherwise, the process may 
re-iterate, by selecting a new value for V.sub.C, e.g.: 
EQU V.sub.C2 =V.sub.SAT -5/4 * (V.sub.DEV +V.sub.CL) 
By the above sketched method, the exposure gain, required to discharge with 
an all-pixels-on pattern to the potential after exposure, is determined: 
EQU V.sub.E =V.sub.SAT -1/4 (V.sub.DEV +V.sub.CL) 
The factors 1/4 and 5/4 are introduced to determine the operation point for 
the potential after exposure V.sub.E in function of the charge potential 
V.sub.C, in order to keep the relative discharge approximately equal. The 
factor 1/4 may more generally be chosen within the range [1/8,1/2]; the 
factor 5/4 changes accordingly. 
The factor of 1/4, may also be dependent on environmental conditions, as 
described below. 
Definition of terms (see FIG. 1) 
The charge potential (V.sub.C 23) of the OPC is defined as the surface 
voltage with respect to ground after charging the OPC by means of a 
charging device 2 such as a scorotron and in absence of any exposure to 
light. The charge potential may be measured by a contact-less 
electrostatic voltage sensor such as a TREK model 856. 
The potential after exposure or discharge potential (V.sub.E 27) is defined 
as the surface voltage of the OPC with respect to ground after charging 
the OPC followed by exposure E.sub.EXP. The potential after exposure may 
be measured by a contact-less electrostatic voltage sensor such as a TREK 
model 856 
The bias potential (V.sub.B 29) is the voltage of the sleeve of the 
magnetic roller 8 of the developing unit 5, with respect to ground. 
The development potential (V.sub.DEV 30) is the difference V.sub.DEV 
=V.sub.E -V.sub.B between the potential after exposure V.sub.E 27 and the 
bias potential V.sub.B 29. When this value is negative, it is regarded as 
`not-developing` and considered as set to a value of 0. 
The cleaning potential (V.sub.CL) is the difference V.sub.CL =V.sub.B 
-V.sub.C between the bias potential V.sub.B and the charge potential 
V.sub.C and is preferentially regarded as a fixed value. 
the saturation potential (V.sub.SAT) is the residual potential on the OPC, 
after a charge cycle followed by exposure with a limitless intensity value 
E.sub.EXP. For every charge potential V.sub.C there is a constant value 
for V.sub.SAT. 
toner supply (TS): the amount of toner supplied to the developing gap 28 
per second. TS is dependent on toner concentration TC, doctor blade 
distance, speed of the magnetic roller 8, etc. 
toner concentration (TC): ratio of amount of toner to amount of carrier in 
the developing unit 5. 
PID controller: Proportional, Integral and Differential controller, 
referring to a general control method, incorporating one, two or three of 
these techniques, as described in `Modern Control Engineering` by K. 
Ogata, Prentice-Hall, Inc., Englewood Cliffs, N.J. 
Overall control strategy and operating point definition 
In order to fully understand the concepts of the invention, it is important 
to describe the global process control subsystem that encapsulates these 
concepts. Referring to FIG. 3, the main goal for the process control 
subsystem is trying to maintain the required maximum density. To achieve 
this the engine 74 develops a small rectangular image or patch, in which 
every pixel is given the same exposure intensity E.sub.EXP. Such a patch 
77 is referred to as a full density patch. The density 76 of the full 
density patch on the photosensitive element 1 is measured by the density 
sensor 6 and compared with the target maximum density 75 by means of the 
comparator 71, generating an error signal 78. This error signal 78 is 
input to a controller 73, such as a PID controller which computes the 
required development potential (V.sub.DEV).sub.MAX to achieve the maximum 
density 75 of the full density patch 77. From this required development 
potential, referred to as (V.sub.DEV).sub.MAX, the process controller 72 
computes the required values for the charge potential V.sub.C, the bias 
voltage V.sub.B and the maximum exposure energy level E.sub.MAX. It 
thereby uses the following rules: 
a fixed value is set for the cleaning potential V.sub.CL leading to the 
restriction that: 
EQU V.sub.CL =V.sub.B -V.sub.C (1) 
since V.sub.DEV =V.sub.E -V.sub.B, the required (V.sub.DEV).sub.MAX value 
leads to: 
EQU (V.sub.DEV).sub.MAX =(V.sub.E).sub.MAX -V.sub.B (2) 
the discharge characteristics of an OPC obey the following mathematical 
law, wherein E.sub.REF is a relaxation constant typical for a certain type 
of OPC: 
##EQU1## 
(V.sub.E).sub.MAX, which is the value of the potential after exposure 
V.sub.E to a maximum exposure energy level of E.sub.EXP =E.sub.MAX, i.e. 
the exposure intensity E.sub.EXP needed for (V.sub.DEV).sub.MAX, has to 
conform with the following restriction 
##EQU2## 
The above restriction is referred to as the K-rule. K is a measure for 
indicating how close to full saturation the OPC is discharged for 
obtaining the maximum density, wherein 0&lt;K&lt;1, 0 being the closest to 
saturation. K is set at a value low enough for getting far enough into 
full discharge. High enough in order not to waste light energy. Typically 
K is set at a value around 0.2, or 0.25 as in the previous embodiment. The 
set of expressions (1) to (4), contains four unknown variables i.e.: 
V.sub.C, V.sub.B, (V.sub.E).sub.MAX and E.sub.MAX. This set of equations 
therefore has only one solution, defining the operating point of the 
engine. 
The solution for the charge voltage V.sub.C is the required charge voltage 
of the OPC. To achieve this voltage V.sub.C the charging device 2 or 
scorotron must be set at a specific voltage V.sub.GRID. It is described 
below in accordance with FIG. 4 how V.sub.GRID may be set in order to 
effectively achieve the required charge potential V.sub.C on the 
photosensitive element. 
The solution for the bias voltage V.sub.B gives the bias voltage to be 
applied directly to the toner supply roller. 
The solution E.sub.MAX gives the maximum exposure energy level to be 
generated by the exposure device 3 in order to achieve the full density 
patch 77. This energy level E.sub.MAX may be realised by electrical 
voltage control or electrical current control of the exposure device 3, by 
amplitude modulation of the electrical signal or by time modulation, or 
other techniques that are well known in the art. 
The solution (V.sub.E).sub.MAX may not be controlled explicitly, since it 
is coupled to the other substantial variables via discharge 
characteristics of the photosensitive element as modeled by the 
mathematical law (3). 
By applying a K-rule, the point of discharge at maximum exposure energy 
E.sub.MAX is always put on the same relative position of the sensitometric 
curve of the OPC. This gives some improvement on the control of changes in 
pixel size as illustrated in FIG. 5, FIG. 6, FIG. 7 and FIG. 8: 
FIG. 5 shows a profile 60 and 61 of deposited mass for one pixel; 
FIG. 6 shows two development curves 62, 63; 
FIG. 7 shows the discharge curve 64 of the OPC at a relative humidity 
RH=30%, along with the bias voltage V.sub.B =-220 V on the vertical axis 
and the corresponding maximum exposure energy level E.sub.MAX =16 
mJ/m.sup.2 on the horizontal axis. 
FIG. 8 shows the discharge curve 65 of the OPC at a relative humidity 
RH=70%, along with the bias voltage V.sub.B =-305 V on the vertical axis 
and the corresponding maximum exposure energy level E.sub.MAX =15.5 
mJ/m.sup.2 on the horizontal axis. 
According to FIG. 5, a maximum deposited toner mass (M/A).sub.MAX =0.7 
mg/cm.sup.2 is selected to achieve the maximum microscopic density. 
FIG. 6 shows two development curves M/A=f(V.sub.DEV). The first and 
steepest development curve 63 corresponds to development achieved at a 
relative humidity RH=30%. From curve 63 it can be derived that in order to 
achieve a deposited toner mass (M/A).sub.MAX =0.7 mg/cm.sup.2, at a 
relative humidity RH=30%, the development potential must have a value of 
(V.sub.DEV).sub.MAX 117 V. Since: 
(V.sub.DEV).sub.MAX =117 V is known, 
the value for the cleaning voltage V.sub.CL being independently selected 
for optimal system performance; and 
the saturation potential V.sub.SAT and the relaxation constant E.sub.REF 
being fixed by the system configuration, and 
since a fixed value for K in the K-rule is selected, the four unknown 
variables: 
V.sub.C : the charge potential; 
V.sub.B : the bias potential; 
(V.sub.E).sub.MAX : the maximum potential after exposure; and, 
E.sub.MAX : the maximum exposure energy level to achieve the required 
maximum density level or the maximum deposited toner mass (M/A).sub.MAX 
may be computed by solving the above set of equations (1) to (4). 
For (V.sub.DEV).sub.MAX =117 V, the following values are obtained 
V.sub.C =-320 V; 
V.sub.B =-220 V; 
(V.sub.E).sub.MAX =(V.sub.DEV).sub.MAX +V.sub.B =-103 V; and, 
E.sub.MAX =16 mJ/m.sup.2. 
The above values are represented in FIG. 7, which shows the preferred 
discharge curve 64 for a relative humidity RH=30%. The electrophotographic 
engine according to the current invention, working under the above 
mentioned conditions, i.e. with the given values for V.sub.C, V.sub.B and 
E.sub.MAX and at a relative humidity RH=30%, will produce a microdot 
having a profile as shown in FIG. 5 by the curve 61. Since, according to 
the spatial energy distribution profile shown in FIG. 9, the maximum 
exposure E.sub.MAX is only applied to the centre of the microdot, the 
maximum required toner mass (M/A).sub.MAX will be present only at the 
centre of the microdot, or at the place where the distance from the pixel 
centre .DELTA..sub.C =0 .mu.m. Since, as shown in FIG. 9, the intensity of 
the light beam decays towards the borders of the microdot, the deposited 
toner mass M/A also decreases if the distance from the pixel centre 
.DELTA..sub.C increases, and no toner mass is deposited at a distance 
larger than 25 .mu.m from the centre of the pixel or microdot. 
In order to assess what happens at a relative humidity RH=70%, one may 
start from the second development curve 62 in FIG. 6. From this 
development curve 62, it is clear that the maximum required toner mass 
(M/A).sub.MAX =0.7 mg/cm.sup.2 may be achieved too, but now a larger 
maximum development potential (V.sub.DEV).sub.MAX is required. From curve 
62 in FIG. 6 it follows that (V.sub.DEV).sub.MAX =183 V at a relative 
humidity RH=70% in order to achieve a required maximum deposited toner 
mass (M/A).sub.MAX =0.7 mg/cm.sup.2. As described above, with this value 
of (V.sub.DEV).sub.MAX =183 V and with the same K-value as above, the set 
of four equations (1) to (4) may be solved to give the following results, 
which are visualised on the discharge curve 65 in FIG. 8: 
V.sub.C =-405 V; 
V.sub.B =-305 V; 
(V.sub.E).sub.MAX =(V.sub.DEV).sub.MAX +V.sub.B =-122 V; and, 
E.sub.MAX =15.5 mJ/m.sup.2. 
With the above settings and at a relative humidity RH=70%, a microdot may 
be imaged by the engine. This gives a profile 60 as shown in FIG. 5. Again 
as for profile 61, the maximum deposited toner mass is achieved only in 
the centre of the pixel, whereas the deposited toner mass M/A decays 
towards the borders of the pixel. 
As one can see in FIG. 5, the change in pixel size is less conspicuous than 
the change in pixel size as shown in FIG. 12, but for high quality 
printing engines the change in pixel size is still not acceptable. 
Therefore, in a preferred embodiment, K is not kept constant but made 
dependent on the relative humidity RH or charge potential: 
EQU K=f(RH, Vc) (5) 
This gives a significant improvement on the control of pixel size as 
illustrated in FIG. 13. The relationship f in expression 5 can be 
determined experimentally, the criterium being substantially constant 
pixel size in the final image, at any relative humidity RH. In the current 
embodiment, the rule used for the result in FIG. 13 is: 
EQU K=0.2+0.0038 .(RH-50) 
To achieve the results shown in FIG. 13, the same procedure as sketched 
above in conjunction with FIG. 5, 6, 7 and 8 is used. In order to achieve 
(M/A).sub.MAX =0.705 mg/cm.sup.2, as shown on top of the curves for the 
pixel profiles 39 and 40 for RH=30% and RH=70% respectively, the required 
(V.sub.DEV).sub.MAX may be derived from the development curves 45 and 46, 
shown in FIG. 14, representative for the toner mass M/A as a function of 
the development potential V.sub.DEV for a device operating at a relative 
humidity RH=30% and RH=70% respectively. As shown on FIG. 14, in order to 
achieve (M/A).sub.MAX =0.705 mg/cm.sup.2, the development potentials as 
shown below are required: 
(V.sub.DEV).sub.MAX =118 V for the device operating at RH=30%; and, 
(V.sub.DEV).sub.MAX =189 V for the device operating at RH=70%. 
With (V.sub.DEV).sub.MAX =118 V and with K=0.2+0.0038 *(30-50)=0.124, 
the above equations (1) to (4) are solved and give as solution; 
V.sub.C =-310 V; 
V.sub.B =-210 V; 
(V.sub.E).sub.MAX =(V.sub.DEV).sub.MAX +V.sub.B =-92 V; and, 
E.sub.MAX 32 20 mJ/m.sup.2. 
This situation, according to a relative humidity RH=30%, is represented in 
FIG. 15. 
For a relative humidity RH=70%, according to a preferred embodiment of the 
current invention, the set of four equations is solved with another 
K-value, i.e. K=0.2+0.0038 *(70-50)=0.276 and, according to FIG. 14, with 
(V.sub.DEV).sub.MAX =189 V. The solution of the equations is given below 
and represented in FIG. 16: 
V.sub.C =-435 V; 
V.sub.B =-335 V; 
(V.sub.E).sub.MAX =(V.sub.DEV).sub.MAX +V.sub.B =-146 V; and, 
E.sub.MAX =12.8 mJ/m.sup.2. 
The value of K has thus an important influence on the operating point of 
the process. The resulting profiles are shown in FIG. 13. It is clear that 
the profiles at relative humidity RH=30% and RH=70% are almost equal, 
which results in a stable reproduction process, even for a relative 
humidity varying within a wide range. 
The required charge potential V.sub.C on the photosensitive element is 
controlled preferentially by means of a closed loop control system as 
shown in FIG. 4. The OPC is charged by the scorotron 2 to a charge voltage 
level V.sub.C. No energy is applied to the OPC by the exposure device 3, 
such that the OPC is not discharged and keeps the voltage V.sub.C. By 
means of the electrostatic voltage sensor 4 the effective charge level 
(V.sub.C).sub.eff 67 on the photosensitive element is measured and 
compared by means of the comparator 82 to the target value 
(V.sub.C).sub.target 68. This target value (V.sub.C).sub.target is 
preferentially computed by the above described control algorithm based on 
equations (1)-(4). The resulting error signal 69 is input to a PID 
controller 81, calculating the required value for V.sub.GRID. V.sub.GRID 
is the voltage applied to the grid of the charging device 2 (scorotron), 
in order to achieve the target charge potential. 
Having described in detail preferred embodiments of the current invention, 
it will now be apparent to those skilled in the art that numerous 
modifications can be made therein without departing from the scope of the 
invention as defined in the following claims.