We present a new application and current results for extending depth of field using wave front coding. A cubic phase plate is used to code wave fronts in microscopy resulting in extended depths of field and inexpensive chromatic aberration control. A review of the theory behind cubic phase plate extended depth of field systems is given along with the challenges that are face when applying the theory to microscopy. Current results from the new extended depth of field microscope systems are shown
©1999 Optical Society of America
In the past few years, research experiments have verified the use of a cubic phase plate, developed in the Imaging Systems Laboratory, to extend the depth of field or depth of focus of optical/digital imaging systems[1,2,3]. The cubic phase plate extends depth of field by encoding object wavefront information thus allowing it to pass through the optical imaging system without being lost to defocus. The image that is formed on the detector is an encoded image which, although not an in-focus image, has minimum sensitivity to defocus. Raytraces of standard and cubic phase plate (CPP) systems are shown in Figure 1 where the rays are drawn from the exit pupil to a point past the original focal plane. The rays show how an impulse response for a general system would appear unchanged over a longer range with the cubic phase plate sytem as opposed to having a single in-focus plane with the standard system.
Point spread functions for each type of system are shown in Figure 2. The images in 2(a) and (b) are PSFs for a standard imaging system with zero and 10 waves of defocus, respectively. The images in (c) and (d) show the resulting PSFs for the same amounts of defocus after the cubic phase plate has been inserted into the aperture stop of the imaging system. The PSFs are encoded so they do not appear as a standard system, in focus impulse response, but they change very little with increasing defocus, unlike the standard system impulse responses.
After digitally recording the encoded image, digital post-processing restores the entire in-focus image. The result is an image that demonstrates the new system’s increased depth of field (up to 8×) over a standard imaging sytem with the same optical power and same size aperture. This increase in depth of field has also been shown to be useful in correcting some focus related aberrations. Increasing the depth of field, for example, allows the use of inexpensive lenses without the problem of chromatic aberration. The depth of field of the entire image is extended so the problem of different wavelengths focusing at different distances is eliminated.
Using the cubic phase mask to extend depth of field by up to eight times can be compared to decreasing the numerical aperture of the optical microscope system by a factor of eight (changing the exit pupil diameter to 1/8 of its original diameter). An 8× reduction in exit pupil diameter, however, would result in a 64× reduction in optical power through the system. The cubic phase plate system does not require any reduction in exit pupil diameter to extend depth of focus and therefore does not suffer a loss of optical power. There is a slight loss in signal to noise ratio (SNR) when the digital post-processing takes place in the EDF system, but it is small compared to stopping down an aperture. Please see reference  for further information on SNR in extended depth of focus systems.
In this paper we wish to review the work that has been done to date on the application of the cubic phase plate technology to simple low magnification light microscope systems. Section 2. reviews the need for extended depth of field in microscopy as well as some of the problems faced in the application. Section 3. then presents some of our recent preliminary results for extending depth of field and controlling chromatic aberrations. Sections 4. and 5. refer to some potential applications and the future work that still needs to be performed as well as some concepts to be explored.
2. Challenges and Opportunities in Microscopy
Light microscopes present an exciting challenge to the use of the cubic phase plate for extending depth of field and controlling aberrations. The very nature of light microscopes (high numerical aperture (NA) systems) results in very small depths of field. Although most specimens are prepared to be very thin, it can be quite difficult to prepare specimens thin enough for the very high NA objectives and there may be times when researchers desire a thicker specimen preparation to help understand structure or shape of the specimen. In such situations, small depth of field can be a substantial problem. Other problems in microscopy include the field related aberrations such as field curvature, spherical aberration, and chromatic aberration, which can be extremely expensive to correct for in the design of a high quality microscope. Inexpensive student microscopes generally sacrifice image quality when using lower cost components. A low cost alternative to the expensive high quality optical components is found in by using the cubic phase plate to extend depth of field, thus increasing the system tolerance to these focus related aberrations. Recent results have shown the cubic phase plate to successfully extend depth of field and help control chromatic aberration in a simple light microscope systems. The path to successful application of the plate to more complicated, high magnification light microscope systems is, however, still rocky. Reasons for the difficulty include: exact location of and access to aperture stops, high system resolution with respect to CCD detector, extremely tight error tolerances, and digital post-processing algorithm optimization. These are not insurmountable obstacles, they merely have not been resolved at this point. However, the preliminary results for the simple, low magnification systems are promising.
3. Recent Results & Analysis
The original experiments for extending depth of field of optical/digital microscopes were done using a Zeiss KF2 ICS transmitted-light microscope, with some modifications. In order to place the cubic phase plate at the aperture stop of the system a relay system was designed which took the wavefront leaving the objective and formed an image on a CCD. The relay system does not necessarily maintain the optical integrity of the Zeiss components and the quality of the resulting images should not reflect on quality of the Zeiss system. The relay system also reintroduces some chromatic aberrations due to the fact that the entire system is no longer optimized to reduce this aberration. The reintroduced chromatic aberration, however, provides an opportunity for demonstrating how the cubic phase plate can correct for this aberration.
3.1 Extending depth of field
The first step in demonstrating an extended depth of field for low magnification systems was to design a general, low magnification, optical imaging system with an easily accessible aperture stop. A 3× magnification system was designed and built using inexpensive achromatic lenses and simple lens barrels. Images of a feather on a fishing fly were then taken with this system using a clear aperture (for the standard system). The feather was slightly tilted so only part of the feather was in focus at one time using the clear aperture system. The height of each image represents a 3 millimeter range on the feather. Figure 3 (a) and (b) show the resulting images when the system was focused on the front and the back of the tilted feather. The cubic phase plate was then placed into the aperture stop of the optical system causing the resulting intermediate image formed on the CCD as shown in (c). The image in (c) was then processed with a digital filter to produce the extended-depth-of-field image shown in Figure 3 (d).
Next, experiments were performed using the modified Zeiss microscope to image a slide preparation of human hair. Using the microscope’s 10× objective, the system has a depth of field of approximately nine μm, less than the thickness of a piece of hair (this hair averages about 65 μm in diameter). The 10× objective system was first used with a clear aperture to take an image of the hair. Another image was then taken with the cubic phase plate in the aperture stop. These images are shown in Figure 4 (a) and (b). The image in Figure 4 (c) shows the cubic phase plate image from (b) after digital post-processing. The new depth of field of the system is at least 10 times greater than the original depth of field (around 90 μm).
The images in the previously described, simple EDF experiments were taken using broadband illumination and a single CCD chip and are displayed using false monochromatic color intensities (as opposed to grayscale). The experiments in the following section, however, were performed using color filters to take three separate monochromatic images which were then recombined to form the color images.
3.2 Controlling chromatic aberration
Another application of the cubic phase plate to general microscope imaging systems is to control focus related aberrations. The common focus related aberrations in microscopes are usually spherical aberration and chromatic aberration, both of which can be quite costly to fix. The high cost of designing aberration free or low aberration objective/tube/eyepiece optical systems is generally a significant portion of the cost of the whole microscope. One of our goals, therefore, is to use the cubic phase plate to correct for spherical and chromatic aberration, allowing less expensive optical systems to be used, and thus reducing the overall cost of some microscopes without sacrificing optical quality. Situations where this technology could have a large impact include lower level classrooms, veterinary or low cost health clinics, and other laboratory/home environments which could not otherwise afford high quality microscopes. Aside from reducing the cost, microscopes in any price range can use EDF technology to further improve their optical quality if needed.
As shown in Figure 5, when using the cubic phase plate to extend the depth of field of the optical system for each wavelength, the new depths of field overlap creating an overall extended depth of field which is not as large as the extended depth of field for a single wavelength but which is free from chromatic aberration.
To demonstrate the cubic phase plate’s use in controlling chromatic aberration, images of salt (with a blue dye) were taken using the modified Zeiss microscope with its 5× objective and the extension tube which has chromatic aberration. Separate red green and blue images were taken using 100 nanometer bandwidth color filters over the light source for both the standard and cubic phase plate aperture systems.
The images in Figure 6 were taken with a clear aperture 5× objective microscope system using 100 nanometer bandwidth red, green, and blue color filters with 650 nm., 550 nm., and 450 nm. center wavelengths, respectively. The blue, green, and red images all have different centers of focus due to the chromatic aberration of the system. The center of focus for green is 32 μm from that of blue and the center of focus for red is another 10 μm further. The overall depth of field of the system for each color is also quite short (approximately 40 μm for blue, 45 μm for green, and 50 μm for red); compared to the height of the salt crystals so only certain planes in the salt crystals appear in focus in each image. The cracked look in these images is due to the blue dye used on the salt crystals. Figure 7 (left) shows the combination of the three standard system images from Figure 6 resulting in the standard system full color image. Figure 7 (right) shows the combination of the three separate color images taken with the cubic phase plate inserted at the aperture stop, after digital post-processing. Note how the chromatic aberration problems have been eliminated and the depth of field has been extended by using the cubic phase plate. The new depth of field is at least equal to the height of the salt crystals (which are a little over one-half millimeter in height) which implies an extension in the depth of field of approximately 10 times or more.
The applications of this extended depth of field microscopy range from providing higher quality images in the classroom to providing faster acquisition of large amounts of information in high end research microscopes. For example, in high quality research microscopes, gathering information about a specimen over a range of depth usually requires several images, each one taken with the focus adjusted to a new plane in the specimen. This procedure is both time consuming and usually results in large amounts of redundant data. Types of microscopes that could benefit from the EDF technology include stereo microscopes, and wide-field fluorescence microscopes, as well as simple reflection and transmission microscopes. The design of an inexpensive student microscope free of chromatic and spherical aberrations could eventually lead to the improvement of higher end microscopes, without increasing cost. Three dimensional microscopy may benefit from EDF technology by allowing more information to be gathered in each image taken through the microscope and used to reconstruct the stereo or 3-D image. Collaborators at the University of Sydney are currently exploring applications of EDF technology to fluorescence microscopy.
One application which has been an inspiration to embark on this particular area of research, is diagnostic cytology. In diagnostic cytology, thousands of tissue samples are quickly scanned and examined for diseased cells using optical/digital microscopes. As different samples on different slides with different preparation thicknesses are passed through the microscope, the placement of the slide in relation to the focal plane of the microscope must constantly be adjusted or potentially life-saving information will be missed. Many optical and digital correlation schemes are used to detect diseased cells, but the variations in focus between each slide must either be adjusted by a human operator or by an auto focus system, thus increasing the time that must be spent on each slide and the probability of imaging or detection error. By extending the depth of field of a diagnostic microscope with a cubic phase plate, the automated detection process can be faster, more efficient, and less likely to miss any important information.
Another potential application of EDF technology is inspection of integrated circuit boards in manufacturing situations. Many fields of material processing can also benefit from extended depth of field.
5. Future Work/Conclusions
Continuing research both at the University of Colorado and the University of Sydney is turning up promising results for extended depth of field technology applications to microscopy, but there is still a large portion of the work left to be done. The many different types of microscopes and hundreds of different applications of each type each offer additional questions about the appropriate application of EDF technology. Some of the topics to be addressed in the immediate future, however, include video rate image acquisition and filtering for all types of microscopy, EDF for metallurgical (long working distance) reflection mode microscopy, the different effects of sampling rate on the overall general EDF system, etc.
This work was funded in part by the Army Research Office under ARO Grant DAAG55-97-1-0348.
References and links
1. S. Bradburn, E. R. Dowski Jr., and W. Thomas Cathey, “Realizations of focus invariance in optical-digital systems with wave-front coding,” Appl. Opt. 36, 9157–9166 (1997). [CrossRef]
3. Imaging Systems Laboratory, www.colorado.edu/isl
4. H. B. Wach, E. R. Dowski Jr., and W. Thomas Cathey, Control of chromatic focal shift through wavefront coding,” Appl. Opt. 37, 5359–5367 (1998) [CrossRef]