Business Segments and Geographic Information - Segment Information (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 28, 2024	Sep. 30, 2023	Sep. 24, 2022
Segment Reporting Information [Line Items]
Total revenues:	$ 4,030.3	$ 4,030.4	$ 4,862.8
Operating income (loss):	882.6	668.4	1,640.2
Depreciation and amortization:	309.0	323.4	430.1
Capital expenditures:	130.2	150.2	127.2
Identifiable assets:	9,156.0	9,139.3	9,071.2
Diagnostics
Segment Reporting Information [Line Items]
Total revenues:	1,782.0	1,880.1	3,018.5
Operating income (loss):	303.1	193.9	1,359.4
Depreciation and amortization:	218.8	224.7	274.0
Capital expenditures:	80.2	85.2	96.8
Identifiable assets:	2,431.3	2,596.4	2,881.7
Breast Health
Segment Reporting Information [Line Items]
Total revenues:	1,522.9	1,432.7	1,227.8
Operating income (loss):	394.5	273.0	183.2
Depreciation and amortization:	41.6	50.0	58.8
Capital expenditures:	30.9	41.1	14.6
Identifiable assets:	1,588.9	1,170.1	1,245.8
GYN Surgical
Segment Reporting Information [Line Items]
Total revenues:	641.3	604.2	522.9
Operating income (loss):	185.5	188.9	104.9
Depreciation and amortization:	48.1	48.0	96.6
Capital expenditures:	16.6	17.0	12.8
Identifiable assets:	1,419.9	1,455.4	1,461.5
Skeletal Health
Segment Reporting Information [Line Items]
Total revenues:	84.1	113.4	93.6
Operating income (loss):	(0.5)	12.6	(7.3)
Depreciation and amortization:	0.5	0.7	0.7
Capital expenditures:	1.4	0.8	0.3
Identifiable assets:	48.3	33.7	27.5
Corporate and Other
Segment Reporting Information [Line Items]
Capital expenditures:	1.1	6.1	2.7
Identifiable assets:	$ 3,667.6	$ 3,883.7	$ 3,454.7