a, Schematic of imaging approach. Top, oligo species involved in labelling. To minimize costs, only two oligo sequences carry fluorophore labels: a fiducial oligo labelled with a Cy3 dye and an imaging oligo labelled with a Cy5 dye. Sequence-specific binding is achieved by in situ hybridization of the primary probes to the genomic DNA. Each primary probe consists of a 40-nt targeting region, a 20-nt arm to bind the fiducial oligo, and a 20-nt barcode to bind the readout oligo. Each barcoded region has at least 20 primary probes, to facilitate detection. Other relevant oligo species include a readout oligo for each barcode (Supplementary Table 5) and a strand-displacement oligo for each barcode (Supplementary Table 6). Bottom, data acquisition sequence. The fiducial oligo binds all primary probes and remains bound throughout the experiment. This enables image registration in the downstream image analysis. The readout oligo binds its target barcode ‘1’ and the Cy5 imaging oligo. The now fluorescent barcode ‘1’ is imaged simultaneously with the fiducial Cy3 signal in 3D. The readout oligo ‘1’ is removed by its corresponding strand-displacement oligo, removing the Cy5 signal. This process repeats for the rest of the barcodes. b, Efficient removal of fluorescent signal by strand displacement: top, the fluorescent Cy5 signal from labelled barcode ‘1’ and the corresponding Cy3 signal from the fiducial channel. Bottom, the same region after treatment with the strand-displacement oligo. Centre panels show the Cy5 channel in increased contrast, showing that all the Cy5 fluorescent signal is removed. Notably, the Cy3 image is unchanged. Similar results were obtained in 6,933 cells analysed. c, Violin plots of the error in nanometres along each image axis, determined as the difference between the original measurements and measurements repeated at the end of the experiment. Red line marks the median, black marks the mean. Distribution of errors based on five repeated barcode-position measurements, n = 163,810 repeated barcodes (left). Distribution of errors from measurement of a single barcode’s position where the original and repeated measurements are separated by less than one hour (h), n = 31,506 repeated barcodes (centre). Distribution of errors from measurement of a single barcode’s position when the original and repeated measurements were separated by the entire experiment lasting 96 h n = 40,032 repeated barcodes (right). N.S. indicates no statistically significant increase in the 3D error (P = 0.8, one-sided Wilcoxon test). d, Correlation between the replicates of ORCA experiments with both 10-kb barcode resolution (top) and 3-kb barcode resolution (bottom) when measuring contact frequency (left) and distance (right). Pearson’s correlation coefficient, r, is indicated. e, Pearson’s correlation of contact frequency measured by ORCA and published Hi-C measurements23 for the 10-kb and 3-kb resolution probesets. f, Pearson’s correlation coefficient between the 150-nm cutoff (used in the main figures) and alternative cutoff values from 50 to 500 nm. Pearson’s r was computed using all unique pairwise combinations of all barcodes measured (70 barcodes in the 10-kb resolution experiments and 52 in both the 3-kb and 2-kb resolution experiments). Relative interaction frequencies and corresponding structural boundaries observed in the contact frequency maps have little dependence on the precise value of the cutoff. Alternate cutoffs remain highly correlated to one another over a range of values.