Cardinal points and image-object magnification with an accommodative lens implant (1 CU)

Ophthalmic Physiol Opt. 2003 Jan;23(1):61-70. doi: 10.1046/j.1475-1313.2003.00090.x.


A simple mathematical method for the determination of the cardinal points of pseudophakic eyes after implantation of an accommodative intraocular lens [posterior chamber intraocular lenses (PCIOL)] is presented. The purpose of this study was to explore the changes during pseudophakic accommodation (PAC) in (1). the positions of the cardinal points, (2). the distance of the object conjugate with the retina, and (3). the image-object magnification. These theoretical accommodation data are compared with clinical measurements.

Methods and patients: Using biometrical measurements of the axial length, equivalent power of the cornea and the anterior chamber depth (ACD) in the non-accommodated state we used linear geometric optics for determination of the cardinal points and object distance as well as lateral magnification (the ratio of image to object size). With the measurement of ACD decrease (following pharmacological stimulation of the ciliary muscle with 2% pilocarpine eye drops) we determined the changes of the cardinal points and magnification to assess PAC amplitude from the shortening of the object distance. Calculated values of PAC amplitude were compared with the respective measured values derived from amplitude measures by accommodometer, defocusing and streak retinoscopy. We analysed the results of a prospective study on 35 eyes of 28 patients after cataract surgery (target refraction: -0.2 D) and accommodative PCIOL implantation (1 CU, Human Optics AG, Erlangen, Germany) 3 months after surgery.

Results: After pilocarpine eye drops, ACD (mean +/- S.D., range; median) decreased by 0.88 +/- 0.48 mm (0.51-1.91; 0.66). Distance of the in-focus object decreased from the non-accommodated state (-5.62 +/- 1.83 m, -25 to -1.1; -4.83 m) to the accommodated state (ACD decrease) (-0.81 +/- 0.21, -2.11 to -0.65; -0.79 m). For a theoretical ACD decrease of 1.0 mm (the intrinsic limitation of the PCIOL design) it was -0.59 +/- 0.28, -1.31 to -0.51; -0.63 m and resulted in an objective accommodative response of 1.49 +/- 0.16, 1.21-1.81; 1.46 D, depending on the actual geometry of the individual eye. On average, magnification as induced by PAC in contrast to that induced by adequate spectacle addition differed by only about 1%. Accommodation measured with defocusing and the accommodometer correlated significantly with the theoretical value based on IOLMaster measurement of ACD decrease (r = 0.752, p = 0.005 and r = 0.676, p = 0.02). Likewise, accommodation measured with streak retinoscopy correlated weakly with the theoretical value based on IOLMaster ACD decrease (r = 0.465, p = 0.05).

Conclusions: Using geometrical optics, PAC can be derived from the biometric data of the eye and the measured ACD decrease. This approach may be an additional indicator for the accommodative response in pseudophakic patients and may allow a subdivision of the measured accommodation into true PAC and pseudoaccommodation, for example, because of increased depth of focus induced by pupillary constriction.

MeSH terms

  • Accommodation, Ocular*
  • Aged
  • Biometry
  • Cataract Extraction
  • Computers
  • Female
  • Humans
  • Male
  • Miotics
  • Models, Biological
  • Pilocarpine
  • Pseudophakia*


  • Miotics
  • Pilocarpine