Generally speaking, nail polish and acrylic nails do not affect the readings of modern state-of-the-art pulse oximeters. This has been proved by many recent researches. Many published papers can be found on the website National Center for Biotechnology Information which is operated by the National Library of Medicine and the National Institutes of Health in the U.S.A. There are also numerous other resources, either on the Internet or found in published professional magazines, discussing effects of nail polish and acrylic nails to pulse oximeters.
In the early days of pulse oximetry, researchers conducted some trial to verify the effects of nail polish on pulse oximetry. In the tests, a number of adult volunteers had various colors of name brand nail polish applied to their finger nails. Measured data from some commercialized pulse oximeters are analyzed. Cote et al. reported that the reading of SpO2 is significantly lowered by 3% to 6% for those who use blue, green and black nail polish, and then suggested nail polish should be routinely removed before pulse oximetry monitoring.  White and Boyle tested several colored nail polishes and agreed with Cote et al. Meanwhile, Rubin  also found that a blue color fingernail polish decreased SpO2 from 97% to 87%.
However, with the advance of technology, most pulse oximeters can ignore other tissues or nail polish and discern only the absorption caused by arterial blood by examining only the varying part of the absorption spectrum.  Brand et al. tested the effects of colors of enamel nail polish to pulse oximeter readings on 12 healthy nonsmoking normoxic volunteers. The results showed that blue, green and black enamel nail polish which had the most significant impact on pulse oximetry, reported by Cote et al. earlier, does not interfere with pulse oximetry.  The test results of Rodden et al. in 2007 also drew a conclusion that fingernail polish did not cause a clinically significant change in pulse oximeter readings in healthy people. This test involved in 27 healthy volunteers with SpO(2)> or =95%. 
In reference , Hinkelbein et al tested the effect of nail polish on pulse oximeter readings in critically ill patients. Their conclusion is: 'Nail polish does not alter pulse oximetry readings in mechanically ventilated patients to a clinically relevant extent. The mean error of measurement for all colours was within the manufacturers' specified range of 2%.', although black, purple and dark blue nail polish had greatest effect on the readings.
With respect to acrylic nail, Hinkelbein et al showed that acrylic finger nails may affect the measurement of oxygen saturation results depending on the pulse oximeter used and may cause significant inaccuracy. On the other hand, a research conducted by Peters  demonstrated that unpolished acrylic nails do not affect pulse oximetry measurements of oxygen saturation. Patients may not need to remove unpolished acrylic nails before surgery.
To sum up, most commercialized pulse oximeters are not influenced by enamel nail polish while arguments still exist on the impacts of acrylic nails. However, it is necessary to mention that, while it is not possible to test all illness conditions in the researches, it usually depends on doctors' experience and knowledge to determine the situation of using a pulse oximeter.
 Cote CJ, Goldstein EA, Fuchsman NH, Hoaglin DC. The effect of nail polish on pulse oximetry. Anesth Anal 1988; 67:683-686
 White PF, Boyle AW. Nail polish and oximetry. Anesth Anal 1989; 68:545-547
 Rubin AS. Nail polish color can affect pulse oximeter saturation. Anesthesiology 1988;68(5):825
 Brand TM, Brand ME, Jay GD. Enamel nail polish does not interfere with pulse oximetry among normoxic volunteers., J Clin Monit Comput. 2002 Feb;17(2):93-6
 Wikipedia, viewed Mar. 2007
 Rodden AM, Spicer L, Diaz VA, Steyer TE. Does fingernail polish affect pulse oximeter readings? Intensive Crit Care Nurs. 2007 Feb;23(1):51-5. Epub 2006 Oct 24  Hinkelbein J, Genzwuerker HV, Sogl R, Fiedler F. Effect of nail polish on oxygen saturation determined by pulse oximetry in critically ill patients. Resuscitation. 2007 Jan;72(1):82-91. Epub 2006 Nov 13
 Hinkelbein J, Koehler H, Genzwuerker HV, Fiedler F. Artificial acrylic finger nails may alter pulse oximetry measurement. Resuscitation. 2007 Mar 10
 Peters SM. The effect of acrylic nails on the measurement of oxygen saturation as determined by pulse oximetry. AANAJ 1997; 65(4):361-363
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