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Business Combination - Narrative (Details) - USD ($) |  |  |  |  |  |  |  |  | 3 Months Ended | 12 Months Ended |
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Jul. 03, 2023 | Apr. 03, 2023 | Nov. 29, 2021 | Jun. 17, 2021 | Mar. 01, 2021 | Feb. 22, 2021 | Jan. 04, 2021 | Sep. 28, 2020 | Jul. 01, 2023 | Apr. 01, 2023 | Sep. 24, 2022 | Mar. 26, 2022 | Sep. 30, 2023 | Sep. 24, 2022 | Sep. 25, 2021 | Aug. 23, 2020
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Goodwill |  |  |  |  |  |  |  |  |  |  | $ 3,236,500,000 |  | $ 3,281,300,000 | $ 3,236,500,000 |  |
Increase in contingent consideration liability |  |  |  |  |  |  |  |  |  |  |  |  | (14,900,000) | (39,500,000) | $ (6,700,000) |
Impairment of intangible assets and equipment |  |  |  |  |  |  |  |  | $ 174,800,000 |  |  |  | 44,300,000 | 27,700,000 | 0 |
Impairment charge |  |  |  |  |  |  |  |  | 186,900,000 |  |  |  |  |  |  |
JW Medical |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Total purchase price | $ 6,700,000 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
JW Medical | Customer Relationships |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Weighted average amortization period | 5 years |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Normedi |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Total purchase price |  | $ 7,700,000 |  |  |  |  |  |  |  |  |  |  |  |  |  |
Customer relationships |  | 3,000,000 |  |  |  |  |  |  |  |  |  |  |  |  |  |
Contingent consideration |  | $ 1,100,000 |  |  |  |  |  |  |  |  |  |  |  |  |  |
Normedi | Customer Relationships |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Weighted average amortization period |  | 5 years |  |  |  |  |  |  |  |  |  |  |  |  |  |
Bolder Surgical |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Total purchase price |  |  | $ 160,100,000 |  |  |  |  |  |  |  |  |  |  |  |  |
Fair value, discount rate |  |  |  | 16.00% |  |  |  |  |  |  |  |  |  |  |  |
Developed technology |  |  | 73,600,000 |  |  |  |  |  |  |  |  |  |  |  |  |
Customer relationships |  |  | 21,700,000 |  |  |  |  |  |  |  |  |  |  |  |  |
Trade names |  |  | 1,400,000 |  |  |  |  |  |  |  |  |  |  |  |  |
Goodwill |  |  | $ 68,800,000 |  |  |  |  |  |  |  |  |  |  |  |  |
Bolder Surgical | Developed Technology |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Weighted average amortization period |  |  | 10 years |  |  |  |  |  |  |  |  |  |  |  |  |
Bolder Surgical | Customer Relationships |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Weighted average amortization period |  |  | 10 years |  |  |  |  |  |  |  |  |  |  |  |  |
Bolder Surgical | Trade Names [Member] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Weighted average amortization period |  |  | 10 years |  |  |  |  |  |  |  |  |  |  |  |  |
Mobidiag Oy |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Total purchase price |  |  |  | $ 729,600,000 |  |  |  |  |  |  |  |  |  |  |  |
Developed technology |  |  |  | 285,000,000.0 |  |  |  |  |  |  |  |  |  |  |  |
Customer relationships |  |  |  | 20,900,000 |  |  |  |  |  |  |  |  |  |  |  |
Trade names |  |  |  | 20,000,000.0 |  |  |  |  |  |  |  |  |  |  |  |
Goodwill |  |  |  | $ 427,700,000 |  |  |  |  |  |  |  |  |  |  |  |
Impairment of intangible assets and equipment |  |  |  |  |  |  |  |  | 10,500,000 |  | 27,700,000 |  |  |  |  |
Impairment charge |  |  |  |  |  |  |  |  | 186,900,000 |  |  |  |  |  |  |
Mobidiag Oy | Equipment [Member] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Impairment charge |  |  |  |  |  |  |  |  | 12,100,000 |  |  |  |  |  |  |
Mobidiag Oy | Minimum |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Fair value, discount rate |  |  |  | 15.00% |  |  |  |  |  |  |  |  |  |  |  |
Mobidiag Oy | Maximum |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Fair value, discount rate |  |  |  | 19.00% |  |  |  |  |  |  |  |  |  |  |  |
Mobidiag Oy | Developed Technology |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Weighted average amortization period |  |  |  | 11 years 8 months 12 days |  |  |  |  |  |  |  |  |  |  |  |
Impairment charge |  |  |  |  |  |  |  |  | 153,700,000 |  | $ 27,700,000 |  |  |  |  |
Mobidiag Oy | Customer Relationships |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Weighted average amortization period |  |  |  | 9 years 1 month 6 days |  |  |  |  |  |  |  |  |  |  |  |
Impairment charge |  |  |  |  |  |  |  |  | 10,400,000 |  |  |  |  |  |  |
Mobidiag Oy | Trade Names [Member] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Weighted average amortization period |  |  |  | 11 years 7 months 6 days |  |  |  |  |  |  |  |  |  |  |  |
Impairment charge |  |  |  |  |  |  |  |  | $ 10,700,000 |  |  |  |  |  |  |
Biotheranostics |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Total purchase price |  |  |  |  |  | $ 231,300,000 |  |  |  |  |  |  |  |  |  |
Fair value, discount rate |  |  |  |  |  | 18.00% |  |  |  |  |  |  |  |  |  |
Weighted average amortization period |  |  |  |  |  | 10 years |  |  |  |  |  |  |  |  |  |
Developed technology |  |  |  |  |  | $ 160,300,000 |  |  |  |  |  |  |  |  |  |
Trade names |  |  |  |  |  | 2,100,000 |  |  |  |  |  |  |  |  |  |
Goodwill |  |  |  |  |  | $ 80,900,000 |  |  |  |  |  |  |  |  |  |
Diagenode |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Total purchase price |  |  |  |  | $ 155,100,000 |  |  |  |  |  |  |  |  |  |  |
Weighted average amortization period |  |  |  |  | 10 years |  |  |  |  |  |  |  |  |  |  |
Developed technology |  |  |  |  | $ 69,800,000 |  |  |  |  |  |  |  |  |  |  |
Customer relationships |  |  |  |  | 9,200,000 |  |  |  |  |  |  |  |  |  |  |
Goodwill |  |  |  |  | $ 83,500,000 |  |  |  |  |  |  |  |  |  |  |
Diagenode | Developed Technology |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Fair value, discount rate |  |  |  |  | 14.50% |  |  |  |  |  |  |  |  |  |  |
Diagenode | Customer Relationships |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Fair value, discount rate |  |  |  |  | 13.50% |  |  |  |  |  |  |  |  |  |  |
Somatex Medical Technologies |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Total purchase price |  |  |  |  |  |  | $ 62,900,000 |  |  |  |  |  |  |  |  |
Developed technology |  |  |  |  |  |  | 38,000,000 |  |  |  |  |  |  |  |  |
Customer relationships |  |  |  |  |  |  | 1,200,000 |  |  |  |  |  |  |  |  |
Trade names |  |  |  |  |  |  | 900,000 |  |  |  |  |  |  |  |  |
Goodwill |  |  |  |  |  |  | 32,400,000 |  |  |  |  |  |  |  |  |
Net acquired tangible assets and liabilities |  |  |  |  |  |  | $ 9,600,000 |  |  |  |  |  |  |  |  |
Somatex Medical Technologies | Developed Technology |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Weighted average amortization period |  |  |  |  | 8 years |  |  |  |  |  |  |  |  |  |  |
NXC Imaging |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Total purchase price |  |  |  |  |  |  |  | $ 5,600,000 |  |  |  |  |  |  |  |
NXC Imaging | Customer Relationships |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Weighted average amortization period |  |  |  |  |  |  |  | 5 years |  |  |  |  |  |  |  |
Acessa Health |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Contingent consideration |  |  |  |  |  |  |  |  |  |  |  |  | 900,000 |  |  | $ 81,800,000
Increase in contingent consideration liability |  |  |  |  |  |  |  |  |  |  |  |  | $ (14,900,000) | $ (39,500,000) | $ (6,700,000) |
Business Combination, Contingent Consideration, Payments |  |  |  |  |  |  |  |  |  | $ 7,600,000 |  | $ 12,200,000 |  |  |  |

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