= front surface visor power (at water/visor interface);
= back surface visor power (at visor/air interface); nwater = refractive index of water = 4/3; nIV = refractive index of inside visor = 1.586; nair = refractive index of air = 1.00; r1-IV = front surface radius of curvature of inside visor = 124.7 mm; r2-IV = back surface radius of curvature of inside visor = 122.7 mm; and dIV = center thickness of inside visor = 2 mm.
Substituting these values into Eq. 3 yielded front and back surface powers of +2.026 D and −4.776 D, respectively, and an equivalent power of −2.737 D for the water/inside visor/air system. (It is worth noting that simplifying the water/inside visor/air system to a water/air system separated by a single refracting interface with a radius of curvature, r1-IV, would yield a power of −2.673 D, similar to the equivalent power just calculated for the water/inside visor/air system.) Therefore, because the water/protective visor/water system could be modeled as a single layer of water, the equivalent power of the water/inside visor/air system (−2.737 D) represents the total optical power created by the helmet's visors when submerged underwater.
Determination of Underwater Spherical Correction
Based on the previously presented models and calculations, astronauts will need to wear an altered spectacle correction to compensate for the negative power induced by the helmet's visors when underwater. To determine the spherical refraction that should be worn inside the helmet, we can treat the helmet's visors as a single diverging thin lens that has a power of −2.737 D (FHelmet) and is placed at the secondary principal plane of the water/inside visor/air system (located 0.93 mm to the right of the inside visor's back surface). Thin lens approximations may be used sufficiently to determine the spherical correction needed to be worn underwater, FW, at a distance of 60 mm from the inside visor's back surface. This scenario is illustrated in Fig. 6, which depicts two thin lenses separated by a distance, d, of 59.07 mm (representing the distance from the secondary principal plane of the water/inside visor/air system to the spectacle lens plane, or 60 mm − 0.93 mm). The first thin lens represents the water/helmet visors system and has a power of FHelmet = −2.737 D. The second thin lens represents the desired underwater spectacle correction (FW) that is to be determined based on FHelmet and the astronaut's spherical spectacle correction in air, FAir.
As illustrated in Fig. 6a, parallel light that is incident on the first thin lens from a distant object will exit the lens divergent. The virtual image formed at the secondary focal point of the first lens, F′Helmet, becomes a real object for the second thin lens with power FW (Fig. 6b). Because our goal is to calculate the power of the second thin lens (power, FW) based on the astronaut's spherical correction in air (FAir), we can effectively split the second thin lens (FW) into a combination of two thin lenses (F1 and FAir) that are in contact. (These lenses are drawn with separation in Fig. 6b for illustration purposes.)
To produce the vergence at the corneal plane required for proper distance correction, parallel light must be incident on the second new thin lens (or the astronaut's distance spherical correction in air, FAir). Therefore, the purpose of the first new thin lens (F1) is to yield parallel light after refracting light from the intermediate object located at F′Helmet. This goal can be achieved by placing the primary focal point of the first new thin lens (F1) at the intermediate object location. As shown in Fig. 6b, the primary focal length of the first new thin lens (f1) is the sum of the secondary focal length of the water/visors thin lens (f′Helmet) and the distance, d, between the thin lenses representing the water/visors system and the required underwater correction:
The power of the first new thin lens is then
Substituting Eq. 6 into Eq. 4 yields:
As seen earlier, the process of generating Eq. 8 is analogous to performing a vertex distance vergence correction in which the power of the thin lens representing the water/visors system (FHelmet) is translated a distance, d, to the spectacle lens plane. Substituting our known values for d and FHelmet yields a desired underwater spherical refraction of
Equation 9 can now be used to calculate the required underwater spherical lens correction, FW, knowing the astronaut's distance spherical correction in air, FAir.
The validity of this model and its calculations was examined by comparing the underwater spherical lens correction calculated using Eq. 9 with the actual spherical lens correction worn by 10 astronauts when training underwater. (All research on human subjects followed the tenets of the Declaration of Helsinki and was approved by NASA's Division of Space Medicine and the University of Houston's Committee for the Protection of Human Subjects.) Actual spherical lens corrections were determined as follows: A subjective manifest refraction was first performed in air to obtain FAir. As dictated by Eq. 9 and depending on the astronaut's age (i.e., their level of presbyopia) and specific training demands, a spherical power of +2.00 D to +2.50 D was added to the manifest spherical power to obtain the actual spherical correction worn underwater. Based on feedback from the astronaut after the training session, the spherical power could be refined to yield a final underwater spherical correction. This actual value was compared with the calculated underwater spherical correction (FW) predicted by Eq. 9.
As shown in Table 1, there was close agreement between the calculated and actual values, validating these model calculations. The mean magnitude of the difference between the actual and calculated underwater spherical refractions was 0.20 ± 0.11 D with a correlation coefficient of r = 0.971. In 70% of eyes, the magnitude of the difference between the actual and calculated values was <0.15 D [a value that is less than the step size and accuracy with which one can prescribe a spherical correction (0.25 D)]. The largest differences between the actual and calculated underwater spherical corrections were observed in astronauts 5, 6, and 7 (mean difference = −0.36 D), with the actual values worn being less than the calculated values. The differences in these three astronauts were likely due to the fact that they were prepresbyopic with some remaining accommodative amplitude (presbyopic eyes are in bold in Table 1). It is common practice to intentionally undercorrect the younger, prepresbyopic astronauts so that the actual distance spherical correction worn underwater is slightly less than the full calculated value. The younger, prepresbyopic astronauts have sufficient accommodative amplitude to cope with the slight undercorrection when submersed in the NBL. Additionally, the slight undercorrection can create less blur for these eyes while they are on the pool deck (in air). In contrast, the full calculated underwater spherical correction is usually pushed on the presbyopic astronauts due to an absence (or near absence) of their accommodative response. Therefore, presbyopic astronauts typically have less of a difference between the actual and calculated correction values. These concepts were evidenced by the data presented in Table 1, as the mean magnitudes of the difference between the actual and calculated underwater spherical refractions were 0.26 ± 0.13 D and 0.14 ± 0.02 D in the pre-presbyopic and presbyopic astronauts, respectively.
Finally, astronauts should visually experience some minification when wearing their underwater spectacle correction and looking through the helmet visors underwater. The two thin lens system of FHelmet and F1, illustrated in Fig. 6b, effectively acts as a reversed Galilean telescope that the patient looks through with their best spectacle correction in air (FAir). This telescope consists of a −2.737 D powered objective (FHelmet) and a +2.356 D powered eyepiece (F1). The magnification provided by the telescope in its afocal configuration for distance viewing is +0.86×, indicating that an image has the same orientation as the object but is smaller in size. Therefore, the size of an object viewed underwater when the astronaut wears their underwater spherical lens correction (FW) will be slightly smaller than when viewing the same object in air through the astronaut's best spectacle correction (FAir).
We have presented a simple model to calculate the distance spherical correction that must be worn to compensate for the optical power induced when wearing a space suit helmet with curved visors underwater. The model depends linearly on the native distance spherical correction (in air) and can accurately predict the underwater correction as exemplified in a set of astronauts. Moreover, these same methods can be used more generally to calculate the refractive correction that must be worn behind any mask or goggle (such as traditional scuba masks, etc.) when submerged underwater.
We thank Dr. Ray Applegate and Dr. Heidi Hofer for providing comments on the manuscript. Work performed by Drs. Gibson and Strauss was conducted at the National Aeronautics and Space Administration (NASA)'s Johnson Space Center under the Wyle Integrated Science and Engineering Group's Occupational Medicine/Occupational Health Contract, NNJ06HB47C. The views expressed in this article are those of the authors and do not reflect the official policy or position of NASA or the United States Government.
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Keywords:© 2011 American Academy of Optometry
refraction; geometrical optics; optical design; presbyopia; astronaut