Single source/cutoff grid, self-aligned focusing schlieren system

Abstract

A compact focusing schlieren system is presented that eliminates the need for a separate source and cutoff grid. Light is projected through a grid ruling and onto a background, where it forms an image of the ruling. The light from this projected image is then reflected back onto the original grid ruling, with a polarizing prism imparting a small offset between the two. Translation of this prism along the instrument axis provides an adjustment of sensitivity of the resulting schlieren images, equivalent to the knife-edge insertion percentage of a conventional schlieren system. The manipulation of the polarization state of the light through the system allows the projected and reflected light to be coincident, maintaining a small footprint for the system, which can effectively be mounted to the front of an imaging camera. Both small-scale and large-scale systems are demonstrated, with fields-of-view ranging from tens of millimeters to approximately $500~\mathrm {mm}$-square. Because retroreflective material is used, the system is ideal for wind tunnel facilities without optical through-access, and it is demonstrated that windows have little effect on the resulting images, with only a slight reduction in image contrast observed when imaging at normal incidence to a window. The ease of construction and alignment of the system, as well as its conventional-schlieren-comparable image quality, indicates that the system could be used as a replacement of conventional systems where a focusing ability is desired.

Graphical abstract

Appendices

Appendix A. Optional/substituted optics

Not every component in the baseline design of Fig. 3 is required, although their inclusion tends to increase the quality of the images. There are several optional optics and alternatives to the baseline design that can be used, which are discussed here in no particular order.

Different light sources can be used with this system, providing varying levels of final image quality. All data shown in this paper were taken using a $640~\mathrm {nm}$ Cavitar Cavilux HF Laser, but high-quality data were also previously taken with both a white and a red LED (Light Speed Technologies HPLS-36) (Bathel and Weisberger 2021). Using a monochromatic light source will improve the quality of the images, especially for larger-scale systems, since chromatic aberrations through the optics will reduce the sharpness of the projected grid and degrade the overall quality of the resulting images. When using a quartz/quartz Rochon prism, the linear polarization state of different wavelengths will rotate by different amounts due to rotary dispersion (shorter wavelengths rotate more than longer wavelengths). For an account of the rotary dispersion measurements by Biot, see the paper by Lowry (1926). The laser used in this study was linearly polarized, although a polarized light source is not strictly needed because the $\mathrm {LP}^\mathrm {1}$ and $\mathrm {PBS}^\mathrm {}$ ensure the correct polarization of light is reflected onto the instrument axis. Thus, any light source can theoretically be used (unpolarized/any polarization/any wavelength), given that the camera is sensitive to its wavelength, that there is sufficient intensity coupled into the system, and that optics and anti-reflection coatings are designed for those wavelengths.

The $\mathrm {PBS}^\mathrm {}$ is first used to reflect LVP light onto the optical axis and to allow LHP light to pass straight through out of the system into a beam dump (not pictured in Fig. 3). The $\mathrm {CD}^\mathrm {}$ can be optionally replaced with a Fresnel lens with similar results. The $\mathrm {LP}^\mathrm {1}$ is included in the system, oriented vertically, to ensure highly-polarized LVP light is then reflected by the $\mathrm {PBS}^\mathrm {}$, and to minimize the amount of light that is transmitted through the $\mathrm {PBS}^\mathrm {}$ and could scatter, potentially degrading the quality of the final focused schlieren image. Note also that the $\mathrm {LP}^\mathrm {1}$ can itself be rotated to act as a variable intensity attenuator when coupling with the $\mathrm {PBS}^\mathrm {}$. The highest quality polarized light will be obtained with the $\mathrm {LP}^\mathrm {1}$ included due to its high extinction ratio, but good quality images can still be acquired using an unpolarized light source and the $\mathrm {PBS}^\mathrm {}$, although the light intensity throughput will be reduced slightly.

For the return/incoming beam, the $\mathrm {PBS}^\mathrm {}$ transmission axis is horizontally oriented, but the addition of the $\mathrm {LP}^\mathrm {2}$ helps to improve image contrast by further rejection of non-LHP light due to its high extinction ratio. However, the $\mathrm {LP}^\mathrm {2}$ can be removed from the system resulting in only a slight degradation of image contrast. Depending on the type of light source being used, a notch filter (e.g., a laser line filter) can be used to reject any external light that was inadvertently coupled into the system. The laser line filter option can be particularly useful if trying to image a luminescent bow shock, for example, where emission at other wavelengths than the system’s laser wavelength can be filtered out. Another option to avoid ambient light interference is by enclosing the entire system in a housing.

A Ronchi ruling was used as the grid element in this study, and can be easily replaced with other rulings possessing either finer or coarser grid lines. They can also be rotated to provide sensitivity to density gradients in different directions, provided the polarizing prism is rotated along with it. Implementation of a transparent LCD screen as a programmable Ronchi ruling is currently being evaluated by the authors. The polarization manipulation of the light through the system requires an additional optic, but this setup allows for remote changes to the grid, including line size, distribution, rotation angle, and shape adjustments.

The $\mathrm {RP}^\mathrm {}$ is not strictly needed to obtain schlieren images, for without it the system will act as a bright-field schlieren system (shown in case (d) of Fig. 12, and discussed in Sect. 3.7), because the projected grid will be reflected and return along the same path back onto the $\mathrm {RR}^\mathrm {}$, and any shift due to a density gradient will result in a darkening of the image. The quality of these images is not as high as the system operating in its nominal $50\%$ cutoff range, but will result in schlieren images nonetheless (see comparison between images in Figs. 14 and 16). This can be an attractive option if the focusing capability is desired, but an appropriate polarizing prism cannot be obtained. When operating without the $\mathrm {RP}^\mathrm {}$, the $\mathrm {QWP}^\mathrm {}$ optic was used to obtain the high-quality images of Fig. 16. However, for two of the tested $\mathrm {RBG}^\mathrm {}$ materials, the $\mathrm {QWP}^\mathrm {}$ was not needed to obtain the high-quality bright-field schlieren images (due to their reflective polarization characteristics). While a quartz $\mathrm {QWP}^\mathrm {}$ was used for the images shown in Fig. 3.7, $\mathrm {QWP}^\mathrm {}$ film (American Polarizers Inc., APQW92-003-PC-165NM or Edmund Optics, #14-725) has also been used to capture images with the same quality, and presents a substantially lower-cost alternative, especially for larger clear apertures.

In the baseline design, the $\mathrm {RP}^\mathrm {}$ is placed after the $\mathrm {RR}^\mathrm {}$ but before the $\mathrm {FL}^\mathrm {}$, limiting how close the $\mathrm {RR}^\mathrm {}$ can be positioned relative to the $\mathrm {FL}^\mathrm {}$ to achieve larger fields-of-view. The $\mathrm {RP}^\mathrm {}$ can be moved to a position just after the $\mathrm {FL}^\mathrm {}$, but before the window. The $\mathrm {QWP}^\mathrm {}$ (when used) must be located after the $\mathrm {RP}^\mathrm {}$, so it too must be moved; in these situations, using the $\mathrm {QWP}^\mathrm {}$ film can be advantageous. By moving the $\mathrm {RP}^\mathrm {}$ after the $\mathrm {FL}^\mathrm {}$, the $\mathrm {RR}^\mathrm {}$ can then be pushed closer to the $\mathrm {FL}^\mathrm {}$, and high-quality, large field-of-view images are possible.

The operation of the system with five candidate $\mathrm {RBG}^\mathrm {}$ materials was presented in this paper, and based on these results, when operating with the Rochon prism in place, any of the five can be used with good results. Two further tests were also performed, one using a sheet of white paper and the other using retroreflective spray paint (Rust-Oleum), and while low signal-to-noise images were able to be obtained, results without either a retroreflective material or concave mirror were not of sufficient quality for practical use. There are, however, several promising retroreflective paint options that can be tested (e.g., projector screen paint), but were not included in this study.

Appendix B. Polarizing prisms

In this study, four prisms were tested. For the majority of the results presented, a quartz/quartz Rochon prism was used. In Sect. 3.10, a glass-quartz Rochon prism, a MgF$_2$/MgF$_2$ Rochon prism, and a quartz/quartz Wollaston prism were all successfully demonstrated. It was also mentioned previously that bright-field focusing schlieren images can be obtained by removing the polarizing prism altogether, but that the image quality will not be as high as a system with the polarizing prism included. Several other prism options exist, each with their own benefits and drawbacks. Some options will be discussed below in no particular order, and are not limited to only those mentioned here.

The Sénarmont prism is an alternative to the Rochon prism, and behaves in an almost identical manner. The difference is that the output polarization states of the unrefracted and refracted beam are orthogonal to those of the Rochon prism, due to the ${90}^\circ$ rotation of the second-prism-half optic axis orientation.

The prisms mentioned in this section thus far have split the orthogonally-polarized beams such that they exit the prism at an angle relative to each other, one unrefracted and the other refracted. A beam displacer can also be used (e.g., calcite), where the output beams are still orthogonally-polarized, but exit the prism parallel to each other, with a certain offset distance. If this option is used, the offset distance must be specified in the design stage and be matched to the $\mathrm {RR}^\mathrm {}$ line frequency being used, because the adjustability of the system is lost when unable to change the offset distance.

One of the drawbacks of the prisms that split the beams at an angle relative to each other is that the beams are constantly diverging after exiting the prism (although this does provide sensitivity adjustments as mentioned in Sect. 3.4). The drawback of the conventional beam displacer is that the sensitivity adjustment capability is lost. A variable calcite beam displacer, proposed by Brasen et al. (2007), could potentially be fabricated where two pieces of a birefringent material slide relative to each other to provide polarization splitting, parallel beam output, and a variable beam separation distance. A $\mathrm {MgF}_2$ window with the optic axis orthogonal to the clear aperture has also been tested by the authors, where the optic is tilted to obtain displaced beams that run parallel to each other, and where the displacement distance can be changed with varying rotation angles.

Based on the success of the Wollaston prism test in Fig. 20c, the Sanderson prism can theoretically also be used (Sanderson 2005). The benefit of this prism is that it has an adjustable splitting angle, but with the larger clear apertures required for the focusing schlieren system, it may be more difficult to obtain uniform splitting angles over the full region needed, and the four-point loading mechanism will also increase the size of the system.