Continuous waveform driving in multi-color electrophoretic displays
Continuous waveforms for driving a four-particle electrophoretic medium including four different types of particles, for example a set of scattering particles and three sets of subtractive particles. Methods for identifying a preferred waveform for a target color state or a target transition when using a continuous or quasi-continuous voltage driver/controller.
1. A method for driving an electrophoretic medium comprising at least four types of particles, wherein each particle has a different optical property from each other, and each type of particle has a different combination of charge polarity and charge magnitude from each other, the method comprising:
providing a continuous driving waveform for at least 500 ms, wherein the continuous driving waveform as a function of time is of the form:
lim
t
→
x
V
(
T
)
=
V
(
x
)
during the entirety of the continuous driving waveform, wherein V(t) is the continuous driving waveform voltage as function of time and x is a representative value of time, and wherein the waveform includes at least three voltage levels.
2. The method of claim 1 , wherein the continuous driving waveform lasts at least 1 second.
3. The method of claim 1 , wherein the continuous driving waveform has a rate of change of no more than 3 V/ms during the at least 500 ms.
4. The method of claim 1 , wherein during the entirety of the continuous driving waveform a change in the rate of change of voltage as a function of time is less than −1V/ms 2 or greater than 1V/ms 2 .
5. The method of claim 1 , wherein the at least four types of particles include two particles of a first polarity and two particles of a second polarity.
6. The method of claim 1 , wherein the at least four types of particles include three particles of a first polarity and one particle of a second polarity.
7. The method of claim 1 , wherein the optical property is color and the color is selected from the group consisting of white, red, magenta, orange, yellow, green, cyan, blue, violet, and black.
8. The method of claim 1 , wherein at least two types of particles include surface polymers, and wherein each of the two types of particles has a different kind of surface polymer.
9. A method for determining a continuous waveform for driving an electrophoretic medium disposed between a first light transmissive electrode and a second electrode, the electrophoretic medium including at least four types of particles, wherein each type of particle has a different optical property from each other, and each type of particle has a different combination of charge polarity and charge magnitude from each other, the method comprising:
determining a first optical state for the electrophoretic medium;
determining a second optical state for the electrophoretic medium;
backpropagating iterative driving voltages for a frame width across a desired time span from the second optical state to the first optical state while minimizing a cost function based upon a differentiable surrogate model of the electrophoretic medium between the first light transmissive electrode and the second electrode; and
assembling the iterative driving voltages for frame widths to produce a continuous waveform.
10. The method of claim 9 , wherein the first optical state is a current color displayed by the electrophoretic medium.
11. The method of claim 9 , wherein the second optical state is a target color displayed by the electrophoretic medium.
12. The method of claim 9 , wherein the cost function represents a summation of a Euclidean distance between the second optical state and an output of the differentiable surrogate model for each iterative driving voltage used to transition from the first optical state to the second optical state.
13. The method of claim 9 , wherein the cost function is:
cost( V ( t ))=Σ i ( ƒ ( V ( t ), x (0)) i −target i ) 2 .
14. The method of claim 9 , wherein the desired time span is at least 500 ms, and the frame widths are less than 50 ms.
15. The method of claim 14 , wherein the continuous waveform has a rate of change of no more than 3 V/ms during the desired time span.
16. The method of claim 9 , wherein the continuous waveform between the first optical state and the second optical state does not have a change in the rate of change of voltage as a function of time that is less than −1V/ms 2 or greater than 1V/ms 2 .
17. The method of claim 9 , wherein a transition between iterative driving voltages during a frame width is less than or equal to 50V.
18. The method of claim 9 further comprising determining a transfer function for an optical state of the electrophoretic medium as a function of time based on outputs of the differentiable surrogate model for each iterative driving voltage used to transition from the first optical state to the second optical state.
19. The method of claim 18 , wherein the transfer function is based on a voltage applied to the electrophoretic medium as a function of time given an initial state of the system.
20. The method of claim 19 , wherein the transfer function is further based on one or more of ambient temperature, relative humidity, and incident light spectrum.