Nov 9, 2021
Which tools to use when working on a HeadupDisplay?
An automotive headup display or automotive headsup display  also known as an autoHUD  is any transparent display that presents data in the automobile without requiring users to look away from their usual viewpoints. The origin of the name stems from a pilot being able to view information with the head positioned "up" and looking forward, instead of angled down looking at lower instruments.
This blog post introduces the use of OpticStudio tools when designing and analyzing the performance of a Headup Display (HUD).
Description of the HUD
Below is a sketch of the HUD. The LCD display emits light. That light is reflected by the 2 mirrors forming the HUD, then reflected by the windshield and finally enters the driver’s eyes. The driver sees a virtual image on the road giving him indications like for example here the speed.
The driver will move his head while driving. The eyebox is a virtual box that represents the range of the driver’s eye position.
We’ll look at an example HUD system with the following specifications.

Virtual image distance: 2 m

Displays the current speed of the vehicle

Mechanical constraints: the HUD will mainly be constrained by the space available under the dashboard. The windshield will act as a beamsplitter

Eyebox: the position of the driver’s eyes is within a box of ± 50mm in width and ± 20mm in height

Eye pupil: the diameter is 2 to 4mm in bright light and 4 to 8mm in dark. For that study, it will be set to 4mm.

The LCD display size is ± 12.5mm in width and ± 5mm in height

Magnification = 6
Steps to design a HUD
From Virtual Image to Display: the design starts backward in Sequential Mode. Why? Because starting the simulation from the virtual image seen by the driver is convenient. The STOP surface can then be placed at the front of the system at where the eye box is located. A rectangular aperture is placed on the STOP surface to describe the constraints on eye position.
From Display to Virtual Image: Then the system will be reversed in Sequential Mode. This allows to evaluate the “true” performance from the display to the virtual image, that is in the forward direction.
Finally, the system will be converted to NonSequential (NSC) Mode. This provides a more realistic model where users can include stray light analysis. It will display the true image driver sees using the HUD.
In this blog we’ll examine step 1 only. A detailed investigation of steps 2 and 3 can be found in the full Knowledgebase article.
Step 1: From Virtual Image to Display (Backward)
Design Selection
The starting point of the HUD is a folded system; it keeps the size small enough under the dashboard. The HUD is made of two mirrors: one flat and one freeform. Mirrors have the advantage of not adding any chromatic aberrations in an imaging system. The freeform mirror needs to be optimized.
For convenience, a template has been built that contains all the starting elements in place. It contains a freeform model of the whole windshield. The windshield is described as an Extended Polynomial Surface. Let’s see how this file is built.
System Explorer:
Aperture: The Eyebox is the system STOP. Because it represents the range of positions taken by the driver’s eyes: Width = ± 50mm and Height = ± 20mm, a rectangular aperture of this size is attached to the STOP surface.
The Entrance Pupil Diameter (EPD) is then computed as 2 x (sqrt (20^2+50^2)) = 108 mm.
Fields: The Field Type is set as Object Height and the Normalization is defined as Rectangular. In the actual system, the image on the LDC display is magnified by a factor of 6 to form the virtual image. Because the current design is backward, from virtual image to the LCD display, the size of the virtual image can be computed and used as the object height to define field size in the Field Data Editor. The LCD Display dimensions are: Width = ± 12.5mm and Height = ± 5mm. Therefore, the object size should be 6 times of this:
Wavelengths: The LCD display will emit at one wavelength = 0.55µm
Windshield
The whole windshield can be modelled, or only the area of the windshield used by the HUD can be modelled.
To find that “active” area, the Footprint Diagram tool can be used (found under Analyze...Rays & Spots...Footprint Diagram). It displays the footprint of the beam superimposed on the windshield surface:
Windshield model:
The windshield can be described by sequential surfaces, like freeform surfaces, or a nonsequential CAD part. If it is described as a nonsequential CAD part inserted into a sequential system, then the system becomes mixed mode. This works well when modelling the system in the backward direction, from Virtual image to display, but will become problematic when working in the forward direction as the STOP surface is now located after the NonSequential Component surface. This makes ray aiming more difficult and could cause other ray trace issues as well.
In this example the windshield is modelled using an Extended Polynomial surface.
Positioning all the elements
Here is a layout that represents the positions of all the elements:
The placement of the surfaces is done using some nice tools:
The Coordinate Break Return: a Coordinate Break surface can be defined with a Coordinate Return under Surface Properties…Tilt/Decenter. OpticStudio will then calculate the parameters of that Coordinate Break surface so that after this coordinate break surface the local coordinates are identical to (“returned” to) the local coordinates of a previous sequential surface.
The Chief Ray Solve: that Solve calculates tilts and decenters of a coordinate break surface so it’s perpendicular to and centered on the chief ray.
Initial performance
The element that adds aberration in the system is the windshield. By how much?
The system can be simplified to light coming from infinity (eye) and being reflected by a windshield; after reflection the spot diagram can tell us the ray angles in the case of the “true” windshield and in the case an ideal flat windshield (flat mirror).
To analyze the aberration introduced by the windshield mirror, click Analyze...Aberrations...Full Field Aberration. The Seidel aberration tool is not applicable here because it only describes third order aberrations in a rotationally symmetric system.
The FullField Aberration analysis calculates the Zernike decomposition of the wavefront and displays the Zernike coefficients across the full field of view.
The full field of view is defined by the red ensquared settings:
Here is a representation of those field points:
For each field point, OpticStudio will fit the wavefront to a series of Zernike Standard polynomials. The following settings define the fit.
The Aberration setting selects which term to display:
Under aberration, the Primary Astigmatism is calculated from Zernike Standard Term 5 (Z5) and Zernike Standard Term 6 (Z6):
If the Display is set to Icon, the length of the line will give the magnitude and the orientation will give the angle.
For our system the results are:

Defocus: 174.4 waves

Primary Astigmatism: Average across full filed of view: 80.2 waves
The system is initially limited by astigmatism brought by the windshield. The beam is also slightly focused by the windshield. The defocus value is not an issue as the design will focus the beam onto the LCD display, so the design of the HUD will start at correcting for the astigmatism aberration.
Build the Merit Function
The freeform mirror can now be optimized to correct for the aberrations introduced by the windshield. First the Quick Adjust tool under Optimize can be used to add a spherical radius of curvature to our freeform mirror. It gives a good starting point.
Build a default merit function:
The default merit function can be built to optimize for the smallest spot (RMS Spot). The system contains apertures, so the pupil will be sampled with a rectangular array.
The Full Field Aberration can be used here to check the field sampling. Quick variations of aberrations across the field of view may mean that more field points are needed.
Then the other specifications can be added manually with operands at the top of the merit function:
Magnification: one specification is about the magnification. REA* (Real ray coordinate) operands can be added to check the positions of the fields in X and Y on the LCD display. DIVI operands can be used to compute the magnification (ratio of chief ray height on image plane vs object plane). A weight factor of 10 will be placed on these DIVI operands.
Distortion: the last specification is about distortion. It has to be below 2%.
Note: Paraxial calculations like distortion do not always work well with asymmetric systems with coordinate breaks. When using distortion operands, always verify the results make sense. The distortion can be manually checked and/or calculated with the locations of the centroids, using CENX and CENY for the four corners of the field of view.
The merit function is now ready.
Our Freeform mirror is modelled using a Zernike Standard Sag surface with 11 terms. The Zernike polynomials are great for optimizing, but they may need to be converted back to standard polynomials like the Extended Polynomials for manufacturing.
Optimization Variables:
It is critical to select the variables that can correct fr the limiting aberrations of the system during optimization. With the Zernike Standard Sag surface we can optimize any Zernike coeeficient, if needed.
Initially, the system contains 2 variables: Back focal thickness and the Freeform mirror.

Z1 is a piston term; it won’t be used.

Z2 and Z3 are the Tilt terms. The different positions of the elements like the LCD display are fixed, so the Tilt terms won’t be used.
After a first local optimization the Full Field Aberration can be checked:
Average value across the field:
Defocus: 7.8 waves 
We can now investigate the benefit of optimizing more Zenike terms.

Z4 is the Defocus/Field Curvature term and is set as variable.

Z5 and Z6 are the Primary Astigmatism term and are set as variables.
Defocus: 15.0 waves Primary Astigmatism: 9.1 waves Primary Coma: 6.9 wave 

Z7 and Z8 are the Primary Coma terms and are set as variables.

Z9 and Z10 are the Elliptical Coma terms and are set as variables.

Z11 is the balanced Primary Spherical aberration term and is set as variable.
Then one minute of Hammer global optimization:
Result of the Optimization
The results of optimization can be checked. The system has not been reversed yet, so the performances are not “real” performances, but “reverse” performances.
Spot size (blur): the RMS of the spot is below 200µm. It doesn’t give much information; it will be more interesting to check the angular size when the system is reversed.
Astigmatism and Coma: The Full Field Aberration can again be checked to see if the optimization has reduced the Primary Astigmatism. Apart from that aberration, the Zernike terms that are most likely to affect the imaging quality of the HUD are the Coma and the Spherical aberration. The field of view used for the results below is the total field of view. It represents the maximum angular extent viewed by the driver allowing vertical and horizontal head movement within the HUD eyebox. It gives also the disparity seen by two eyes.
The average value across the field is:Defocus: 3.6 waves Primary Astigmatism: 10.7 waves Primary Coma: 2.2 wave 
Astigmatism has decreased from 80 waves to 11 waves. The plot below is using a relative scale; the average value is subtracted from the absolute values. It gives a better idea of the aberration variation across the field of view:
Distortion: just above 2%
Reversing a system is not straightforward. The reverse element tool in the Lens Data Editor has some limitations and a HUD system will certainly break them as the system contains coordinate breaks and nonstandard surfaces.
To learn more on how this can be completed, along with how to export the design to NonSequential Mode for further analysis, click here to read the full knowledgebase article.
Don't miss our upcoming webinar on this topic:
Straylight analysis for head up display
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Author:Sandrine Auriol
Senior Optical Engineer
Zemax An Ansys Company