Optical Delay Line Stages – How Do They Work?

Deep in the hallowed halls of the Paris observatory in the late 17^th Century, a paradigm shift was underway. The speed of light conjectured by luminaries such as Descartes and Aristotle as infinite and instantaneous was empirically showing delays. The revelatory observation of eclipses of the Jovian Moon, Io, had provided a basis for what would become the first practical measurement of the speed of light using an optical delay from a variable path length. Today, very precise path length control in optical delay lines are critical to techniques in transient absorption spectroscopy (using pump-probe), Fourier Transform Infrared Spectroscopy (FTIR), and many other applications.

In time-resolved spectroscopy, dynamic processes in materials and chemical compounds can be studied precisely. With the help of ultra-short pulse lasers, changes can be made visible, with time scales down to the attosecond range. The calculation below shows that a 10nm step in a free space delay line adds a delay of ~.07 femtoseconds (delay in solid materials, such as optical fibers, depends on their optical properties). With this in mind, it becomes clear that in order to control a delay line in the Femtosecond and Attosecond range, nanopositioning capabilities are essential.

In the below diagram, we show the basic operating principle of a free space optical delay line. Here, the path is shown at Position X (green path) and again after a small linear translation to Position X’ (purple path). Note the green path overlaps a portion of the purple path. Let’s use this simple diagram to calculate optical path length difference and corresponding optical delay:

1. X=A+B+C (green path length)

and

2. X’=A+A’+B+C’+C (purple path length)

And path length difference is given by:

3. X’-X=A+A’+B+C’+C – (A+B+C)=A-A+B-B+C-C + A’ + C’ = A’+C’ (but A’=C’, the incremental motion step)

We then obtain:

4. X’-X=2A’

And in the time domain the optical delay is given by:

5. t= 2A’/c (where c is the speed of light)

In simple terms, this shows the direct importance of Minimum Incremental Motion (MIM) capability in the chosen linear translation stage that drives the optical delay in terms of temporal delay resolution. MIM is a standardized motion term that identifies the smallest consistent and reliable step that can be made with the stage.

The very fundamental influence of minimum incremental motion on Optical Delay Line time resolution makes it a guiding specification in PI motion solutions across a number of spectroscopy/microscopy and interferometry applications. In optical delay line applications, the first solution often considered is the V-508 Series of Linear Motor Stages. The direct-drive design, combined with the direct metrology linear encoder eliminate drive train errors such as backlash, play and non-linearities that are often found in screw-drive type linear stages, stepper motors or geared motors.

The V-508 Series of direct-drive precision linear motor stages provide an ideal platform for integration in optical delay lines combining PI proprietary nanopositioning technologies to achieve sub-nanometer resolution and single nanometer MIM.